(18) y "+9y '= sec² 2x %3D (19) y "'+6y "–14y'–104y = -11 le*

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: The path travelled by a long period comet as it passes near the sun is described by a hyperbola.…

A: Given:- The path travelled by a long period comet as it passes near the sun is described by a…

Q: Form the partial differential equation by eliminating the arbitary from z=xy+f(x2+y2)

A: Form the partial differential equation by eliminating the arbitary from z=xy+f(x2+y2)

Q: 4. Form the differential equation representing the family of hyperbola having the center at the…

A:

Q: Solve the partial differential differential by separation of variables 70z + 6 = 0.

A:

Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

A:

Q: . (4x³y5 sin 3x + 3x*y5 cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A: See the solution.

Q: (1) Find the general solution for -) dx - -) dy = %3D

A:

Q: [y²e + √elnx dy-(xy) sin² ( * O) + (---) (-) sin² tan² ,dx ey+Inx dy y(In2x-lny) -ex. dx = 0

A: We can solve this using substitution method of ordinary differential equation

Q: 5 Find xy dydx. 4

A:

Q: 4. |1- sin2y dy 6. y +2)/y- 1) dy (y + 2)/y

A:

Q: fx' = 9x + 7y ly' = 2x + 2y

A: We see that x'y'=9722xy. 9722The eigenvalues of A are the roots of the characteristic equation…

Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: Solve dy/dx =( y+x-2) /(y-x-4) Equation s reducible to homogenous form

A:

Q: Solve the differential eqyations y" – y'+6y =e -2x

A: Differential equation problem.....

Q: 15 dy dt 2-

A:

Q: (cos 2y - 3x²d²)dx + (cos 2y − 2x sin 2y − 2x³y) dy = 0

A: The differential equation is given as cos 2y - 3x2y2dx+cos 2y - 2xsin 2y-2x3ydy = 0 Compare it with…

Q: 2 Express the flowing equation in Cartesian equationr = 1-cos e

A: The given polar equation is: r=21-cosθ

Q: 2 (b) - 2y dx +(2y tan'(x )-2x +sinh (y))dy = 0

A:

Q: 1. Solve (cosxcos y+2x)dx-(sinxsin y+2y)dy=0

A: (cosx cosy + 2x)dx - (sin x siny + 2y)dy = 0 => cosx cosy dx + 2x dx - sin x siny dy - 2y dy = 0…

Q: Show that the solution of the differential equation (1–x*) = 2x(1+ y). dx 1+x given that y=1 when…

A:

Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0

A: We will find out the required solution.

Q: Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete…

A:

Q: 2. sin3x dx + 2y cos 3x dy = 0

A: Given equation - sin(3x)dx+2ycos33xdy = 02ycos33xdy =-sin3xdxydy =-sin3x2cos33xdx             Taking…

Q: 4: Find aun -2 2y² Sin(xy) dx dy

A: Topic:- application of integration

Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: 5. Obtain the Differential Equation from the family of ellipses centered at (h.k) whose semi-major…

A: Given data is: The semi-major axis is twice the semi-minor axis and the center of the ellipse is…

Q: 7. 2r tan y dx + sec² y dy = 0

A:

Q: Find the general solution of the inhomogeneous equation y" + 3y' = te'.

A:

Q: -Tsin(nx)cosh(3y) dx + 3cos(7x)sinh(3y) dy =0

A:

Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

A: Since you have asked multiple questions,we will solve the first question for you . If you want any…

Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

A:

Q: 4. ox x cost at cost of 3 procuct nule J cost dt + cost at [sint] + x CSLX)ま(x) = Sin x - 0 + x cos…

A: To determine ddx∫0x3 x cos t dt.

Q: What are the order and degree of the differential equation representing the family of parabolas y2 =…

A:

Q: y(1-x^2) dy/dx=x(1+y^2) solution of first order Deferential Equation

A: We have to find solution of y(1-x2)dydx=x(1+y2)

Q: Find the differential dy. y = cubic root of 3x^2

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Q: Ssin^3 (2/3 x) cos^4 (2/3 x) dx

A:

Q: Ans: y-x+ In y+3, dy = 7. ху+3x-у-3 dx ху-2x+4y-8

A:

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: Soru 1. (1+ 25)dx + 20* (1 - )dy = 0 ; -) dy = 0 ; + 2ey) dx y(0) = 1,

A: Given that:                           1+2exydx+2exy1-xydy=0    .........................(1)…

Q: х2 9 dy + sinx - у %3D0 dx

A:

Q: ion dy 3t2 dt 2y + 2t3y' tion: ||

A:

Q: 6) S sech (2x - 3) dx 7)S e-e-x e*te-x dx 8) [(eax – e-ax) dx sinh x 9) S 1+coshx dx

A:

Q: ry' = 3y + y? ху

A: Solution of a nonlinear differential equation

Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

A:

Q: The path travelled by a long period comet as it passes near the sun is described by a hyperbola.…

A:

Q: d'y dy dx² dx 21 29 - -6y=6e¹ cos x; when x=0, 20 dy dx =-629 y = 2e-3x - 2e²x 3e-* 29 (3 sin x - 7…

A:

Q: 1) S 2 sec y (tany – sec y) dy

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. sin3x dx + 2y cos³3x dy = 0

A: Given- sin3xdx+2ycos33xdy=0 To Solve- The above differential equation.