Differential Equations Answers

Solve the initial value problem:

𝑥^2𝑦" + 𝑥𝑦′ + 9𝑦 = 0; 𝑦(1) = 2, 𝑦′(1) = 0

Find the general solution of the equation:

𝑥^2𝑦" − 7𝑥𝑦′ + 12𝑦 = 0

Find the solution of partial differentail equation ,whether it is linear,non linear or quazi linear .Uxx+xUy=y

Find the integrating factor and solve the following equations:

( 𝑦 − 𝑥^2) 𝑑𝑥 +( 𝑥^2sin 𝑦 − 𝑥 )𝑑𝑦 = 0

solve (1+t²)y' +4ty=(1+t²)^-2; y(0)=1

y''-y=3x^2e^x

solve the ivp cos(x)y¹ + sin(x)y = 2cos³(x)sin(x) - 1; y(pi/4) =3/2, 0<x<pi/2

find the value of b for which the given equation is exact, and then solve it using that value of b

(xy^(2)+bx^(2)y)dx+(x+y)x^(2)dy=0

Solve y’=y-x2

, y(0)=1, by Picord’s method upto the third approximation . Hence find

the value of y(0,1), y(0,2)

solve the D.E dy/dx = (6x^5-2x+1)/(cosy+e^y)