Differential Equations Answers

Q. Choose the correct answer.
Q. Which of the following is the solution of differential equation du/dx=x^2/(1-u^2 )
i) x3+u3-3u=2
ii) 3/2x3+3/2u3-9/2u=3

iii) -2x3-2u3+6u=4
a. i) only
b. ii) only
c. iii) only
d. i), ii) amd iii)

Q. Choose the correct answer
Q. Which of the following differential equation (with dependent variable y) are linear
(i) (x+y)dy=x2dx+y2dy
(ii) (x2+y)dy=x2dx+ydy
(iii)(x2+y)dy=sin ydx

Solve the following pDEs
A). d²u÷dx²= 8xy²+1
B). d²u÷dxy- du÷dx=6xe^x

The area bounded by a curve, the x-axis, a fixed ordinate, and a variable ordinate is proportional to the difference between the ordinates. Find the equation of the curve.

Solve the below differential equation
y'''+3y''+2y'-5y=sin2t

Change the below differential equation to transfer function
y'''+3y''+2y'-5y=sin2t

Solve the below differential equation using the control and simulation loop. Plot the resulting state variables.



y’’’+3y’’+2y’-5y= sin2t

by labview program

Solving this following ODE by Frobenius Method
X^2y’’+(4x-x^2)y’+(2-x)y=0 full solution step-by-step

solve the equation d2^t/dx2-4t=0

solve the second order differential equation d^2y/dx^2-4y=12x, y(0)=4, y'(0)=1