4. Solve the differential equation 2x(2x – 1) - (x + 1) + y = 0 using the method of Frobenius. dx2

Q: 2. Solve the Second order differential equation d'y dy -4 +11y=e* sin 4x. dx dx?

A:

Q: 3. Find all solutions of the given differential equation. dy xy dx x² + 1

A: Given dydx=xyx2+1

Q: Find the general solution for each of the differential equations given below. Y” + 2y’ + y = e^-1

A: Find the general solution for each of the differential equations given below. Y” + 2y’ + y = e^-1

Q: 1. Solve the differential equation: (x – 2y) dx + (2x + y) dy = 0

A:

Q: 1. Solve the given differential equation (2xy*e" + 2xy" + y)dx+ (x*y*e" – x*y² - 3x)dy= 0

A: The solution is given as

Q: B. Find the general/particular solution of the given higher-order differential equation 5.) dx4 d*y…

A:

Q: (6) Solve the homogeneous differential equation (x – y)dx – 2xy’dy = 0 - |

A:

Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

A:

Q: 1. Solve the differential equation y" + 4y' + 8y =-4e-2 sin(2x) using the method of Undetermine…

A:

Q: _6// Solve the differential equation 2y³dx – (yx? + y³)dy = 0

A:

Q: Solve the differential equation (D³ + 1)y= cos(2x – 1)

A:

Q: 1. Find the general solution of the differential equation: d°y d'y dy , dy - - dx6 dæ3 dx2

A:

Q: Find the general solution of the differential equation (D2+2D+5)y3cos hI = cos

A:

Q: 2. Solve the Bernoulli differential equation y' +y = y2

A:

Q: (4) Find the general solution of the differential equation (D² + 2D + 5)Y = = cos ha

A:

Q: The solution of the differential equation y - 25y = e using the method of reduction of order is

A: y''-25y=e^5x g(x)=e^5x

Q: (4) Find the general solution of the differential equation (D² + 2D+5)y= sin hæ

A:

Q: 3. 3x²y dx - (x³ + y³)dy = 0, y(1) = -2

A: Solution to the differential equation

Q: 1. Solve the given differential equation (2ry* e" + 2xy' + y)dx+ (x°y*e' -x'y' -3x)dy= 0 | |

A:

Q: 3. Get the general solution of the differential equation (x+2y-4)dx- (2x+y-5)dy%3D0.

A:

Q: 1. Solve the following Exact Differential Equation : dx 3 1 (2?y3 - + y = 1 1+ 9x2' dy

A:

Q: 1) Solve the differential equation x² + y² ) dx - :- (ryVx² + y²) dy = 0.

A: the given differential equation is: x3+y2x2+y2 dx-xyx2+y2 dy=0 we have to solve the given…

Q: 22. Solve the nonhomogeneous differential equation y"-2y-15y 2 cos 3x +5e5* + 2

A:

Q: 1. Solve the following differential equation. a) y/1- y² dx + (x/1- y² + y) dy = 0 . |

A:

Q: 3. Solve the given differential equation xy dy - (x2 +y)dx

A: The given differential equation is  xydy - (x2 +y2)dx = 0 (x2 +y2) dx - xydy=0

Q: Q1) A. Solve the First Order Differential Equations of the following 1. dy 3x² e-y %3D dx

A: Given: 1. dydx=3x2e-y The separable differential equation of the form M(y) dy= N(x) dx can be solved…

Q: (10-6y+e-3) dx - 2dy 2dy = 0

A: Given.

Q: 2. 2 ydx + x(x² In y-1)dy=0

A: Solution is given below:

Q: 2: Solve the differential equation (D²-2D+2)y=cos9x.

A:

Q: dy dx + y = 2xy-ex

A:

Q: 4. Solve the homogeneous differential equation x'dy+(y² +xykdx = 0.

A: To solve the given homogeneous differential equation.

Q: 01) Solve the differential equation with the given initial condition: y' - 6x²y + 4xy = y. where…

A:

Q: Solve the given problem (3x?y3 – 5x*)dx + (y + 3x³y²)dy = 0 on Exact First Order Differential…

A:

Q: 2:(y –x² }tx+ dy =0 1.

A:

Q: 1. Solve the differential equation xy dx = (x+2) dy =o

A:

Q: Find the general solutions to the given differential equations y' -  y = xe^2x + 1

A: The general solution of a differential equation is given by y·I.F=∫Q·I.Fdx+c

Q: 1) Find the general solution to the following differential equation, (2xy² – ysin(x) + 2x + 1)dx +…

A:

Q: 4. Using the method of Frobenius, solve the differential equation a²y" +5xy'+3y = 0. %3D

A: Given below the detailed solution

Q: (5) Find the general solution for the differential equation (x² – 2xy – y²)dx – (x + y)²dy = 0.

A: It is a first order non linear ordinary differential equations and also it is a exact equation…

Q: 1) Solve the Bernoulli differential equation with the given initial condition. -2xy = 3y", 0 =.

A:

Q: 3. Solve the differential equation (xr² + y² )dx + xy dy =0.

A:

Q: dy 3(1+x2)=2ry(y3-1)

A:

Q: 4. In the differential equation (y -x -4x-1)dy + 2y(x+ y+2)dx = 0, MN

A:

Q: (6) Find the general solution of the differential equation (D² + 4D+ 8)y = e-2ª cos 2x .

A:

Q: 1. Find the general solution of the given differential equations: y/ - y = x +1

A: We have to solve the given differential equations.

Q: 1. Solve the differential equation (x+y)'dx+(2xy +x -1) dy =0 subject to the initial condition y(1)…

A: Compare with exact differential equation and then check exactness

Q: (d) у" + 6у + 10y 3 е2" e2¤ cos(x)

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.