y"-6y"+2y'+36y = 0

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

A:

Q: Find the set of solutions (3x – 3y – 2) dx – (x – y + 1) dy = 0. - - %3D

A: Given differential equation is linear, we will use substitution to solve it

Q: Evaluate the integral.

A: Integration is a process of finding the anti derivative of a function. There are basically two types…

Q: H2. 2dy dy dr2 d²y dy :1 at x = 0. dx – 52+2y= 2x², y=7 and - dx

A:

Q: Find the particular solution of csc y dx + sec2 x dy = 0; y = π/2 when x = π/2

A: We solve this differential equation by separation of variables.

Q: 3. II Azy'dz dy = 2y°(3² – 1)dy | 2y (y? – 1)dy 1

A: Given that a double integration .We use general  property of integration to solve this integration.…

Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

A:

Q: 1 В(т, п) ym-1(a – y)"-'dy. am+n-1

A:

Q: 10.(x + Jy² + 1)dx – (y-- -(y- |dy = 0. y2+1

A:

Q: 22 2 dy = 1-x +y _xy 2 2 x y dx

A:

Q: Find the particular solution for (2y3 – x³) dx + 3xy² dy = 0 when x = 1, y = 1

A:

Q: 6. (2z – 1)(y – 1)dr + (x+ 2)(x – 3)dy = 0, y(1) = -1

A:

Q: 5. sinx+ cosh2y = 0. dy 6. /2xy -= 0. dy y

A:

Q: 4. (x+ 2y-1)dx-(2x+y-5) dy =o

A: According to question,Given differential equation,x+2y-1dx-2x+y-5dy = 0

Q: 1. y' = e-" (2x – 4) y(5) = 0 2. dy = by°r y (1) = dz 1 25

A:

Q: (a) (Ex) ((Ax --> Bd) --> Ky) (b) (Ex) ~ (Dx v Cy) (c) -(x) (Dy --> (Hx v ~Ga))

A:

Q: S(y* - y-3)dy

A:

Q: 2. (2x + 4y -3) dy + (x + 2y -1) dx = 0; y(2) = 5. Determine y(3)

A:

Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

Q: dy 3 sinh y - 5 cosh y

A: Given, I=∫dy3sinh y-5cosh y

Q: dy=y°-1 ex 2y

A: This is Separable differential equations

Q: dy y dx 2x = 3y2 – 2 when y = 1 and x = 1 in terms of x. %3D - -

A:

Q: 2. ( 3 x - 3 y - 2) dx - (x - y + 1) dy = 0

A:

Q: 1- 2r (1 + y')dx - y (1 + 2x)dy =

A:

Q: y(4x+y)dx-2(x2-y)dy = 0  when x = 1 , y= 1

A:

Q: 10. x = Vt-2, d²y y =t2-3' dx2

A: The given question is taken from the derivative and we have to find the derivative of the parametric…

Q: 2. (2x+4y-3) dy + (x+2y-1) dx = 0; y(2) = 5. Determine y(3).

A:

Q: Intergrate:

A: To evaluate the integral.

Q: (continue solution of de) (2ysinxcosx - y + 2y²e*Y" )dx = (x - sin²x - 4xye*y" )dy

A: Using method of exact differential equation.

Q: y 3D 1 y = secxtanx; y

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: Pdx + dy = 0, y(-1) = 2. (y 2) dy = 0, y(-1) = 2. ry2

A:

Q: Q2. Solve yfrcos (4) + ysin (2)] dx – x [ysin (2) – xcos (2)] dy = 0

A: Here we have to solve the above differential equation  by first checking whether the function is…

Q: 22 32 S[ (4-y ) dydx 1. ans:- 3 0 0

A:

Q: 2-dy dy. y2 dx 12 ナ /2

A: We have to solve the given equation. The given equation is 2-dydX=y2X2+yX+1    ......(1)

Q: LLL- (x+ y+ z)dydxdz. -1 J-1 J-1 |

A:

Q: 14-2x 1. ! ] dydx 0 2 2. dxdy 0 y 11-r 3. dycx o 1-x 4. [[ dydx 0 0

A: Answer 1: changing dy dx to dx dy; limits of integration: 0 ≤ x ≤  [2 - (y/2)] 2 ≤ y ≤ 4

Q: 26. x = 2y, y(1) = 5 dy

A:

Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

A:

Q: 5. y" – 2y' + y = 2sinx cosx y'(0) = 0,y(0) = 0 %3D | -

A:

Q: 3z (sec-(-3z?))³ 2|–3z*|-/9zª–1 If y= sec-1 (-3x²), then dy dz

A:

Q: Vy2 -25 dy S y3

A:

Q: (x-y)dx + (3x+y)dy=0; when x=3, y=-2

A: We need to solve (x-y)dx + (3x+y)dy=0; when x=3, y=-2 The solution is given below.

Q: 2x - y + 5) dx - (2x + y) dy = 0 where x= 3, y=7

A: Let's find.

Q: * 2e² + 6z² – 8z + 6 cosh 3z dz ez + z3 – 2z2 + sinh 3z |

A:

Q: 9-y dy 5. S y

A: We will use trigonometric substitution.

Q: (x - y) dx + (3x + y) dy = 0; when x = 2, y = -1.

A:

Q: dy/dt=0.3(y-200)

A: Separate the variables and integrate both sides.

Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.