1+t? if y' = 3y-y2 for which of the I.C's do we have the guaranteed existence of solution : Select one: a. y(0)=3 b. y(-3)=3 C. y(0)=-3 d. y(3)=D0 e. NOTA

Q: Q6. Find the general solution of the equation: (mzny)p + (nx - ly)q = ly - mx

A: Identify the given partial differential equation and write it in the standard form Pp+QThe given…

Q: (D³ – 3D + 2)y = -7 5.

A: Solve the following

Q: 2. ryy = y² – x²

A:

Q: The linearization of y = (6x- 11)2/3 at a = 2 has the form L(x): = mx +b, Find the values of m and…

A: We have to find out

Q: 1. y = 1+3x-x2

A: Since there are more than one question, only one question is to be answered. A function is given by,…

Q: Q2: Solve T" – c? uT = 0 given c = 3 and u = -1?

A: First I have put the given values into differential equation and then by method find the solution.…

Q: Find a real general solution. x?y" – 2y = 0.

A: The given differential equation is x2y''-2y=0. Clearly, the given DE is a second order Euler…

Q: if y = 3x² – 4r³ + 3ª + VI + a, then dy/dr is:

A: Given that     y = 3x2-4x5+3x+√x+π Here we have to find dy/dx . We know that        dxn/dx = nxn-1…

Q: 411-41 r PV = C - (1+r) ease make r the subject -n-

A: Please see the below picture for detailed solution.

Q: Tgir.y) = (2ry, 1+2+) and g(1.0)=8, then g(4.1)-9(2.1) =

A: Topic:- calculus

Q: Solve for y: x³ + ¹y = xy + 7.

A:

Q: + y²(x+ 1)² = C

A:

Q: Which of the following equations is variable separable? O a y+2zy O b. (z2 + y²)da – aydy = 0 O .…

A:

Q: Solve : (6x + y) dx + y(2x – 3y)dy = 0 xự + 3x? – = c 3æy – 3x? – y = c | - Option 1 Option 2 xy +…

A: We have to solve

Q: 2y³ + y y4 + y² + 1 (e-y. V5+ e-y

A:

Q: 1 1-¹ ( ( 5 + + 2) ³) 3 = Find ac + b. α ~tbeat C

A:

Q: 5x-y2 2xy+3y2" c. xy? - 2x5 + 3y³ = C d. xy? + x5 + y3 = C 29. Find the general solution in implicit…

A: We have to find solution of exact differential equation.

Q: 2 - ry + y + 1 1 y = +x - 1; y" =

A:

Q: Find the four solutions of the equation z* - 4z? + 16 = 0.

A: z4-4z2+16=0

Q: When x = 2s+7t, y=5st and z= 3.x2 – 3, in the form of s and t. express

A:

Q: Find the general solution of tx -3x = t³+2t for t> 0.

A: Given DE is  tx'-3x=t3+2t .......(1) We find the general solution of (1).

Q: 2 (0² 20 0 Ans v=c₁ +c+.

A:

Q: x2 dx+(x3+y6+2y5)dy Give an implicit solution

A: we need to find out the solution of the differential equation.

Q: y" – y = 2xe". Y' %3D

A:

Q: You are monitoring the movement of a 2D alien. After months of analysis, you have come up with a the…

A:

Q: d. x+3y = 0 y-4+ 4(x - 2) f. -6x + 4y -7 Find intercent and v-intercent.

A:

Q: 1 4. (1+2)y/ + 2ry = (1+2)y

A:

Q: x° +2 y=- e3x +9

A: Given: As x→∞, y=x6+2e3x+9 To find: limx→∞x6+2e3x+9

Q: Find the general solution of æ²p+ y²q = (x + y)z.

A:

Q: = / y ²³. (X²+1) (3x+4) 5/ (2x-3)(x²-4) Find dy da

A: To find dydx:

Q: x²y+ 2xy = x + y ise y =?

A:

Q: dy (b) +7• y= ÷; y (0) = 1 dr The answer is y

A:

Q: Find the particular solution of

A:

Q: Evaluate | (r + y)ds, c : x 3t, y = - 3t + 3, for 0 <t< 3.

A: Given: ∫C(x+y)ds, C: x=3t, y=-3t+3, for 0≤t≤3

Q: cln3 dx (b) (10 points) Ф) (10 роints) z et n2 e*-e

A: We use the definition of the integral of functions and partial fractions to evaluate the given…

Q: Which of the following equations is variable separable? O a. (3a2 – y²)dx – 2aydy = 0 O b. (z² +…

A:

Q: 2 V4-x2 e*²+y* dydx =? -2 0

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.