Question

Solve the differential equation:

a) y'= t^2y^3 / t^3+6

b) y'= x(e^x^2 +2) / 6y^2 ; y(0) =1

Answer #1

Solve the second order differential equation
y'' + 6y' + 9y = e^(-3t) + t^(3)

Solve the differential equation with initial value
y''−2y'+y=e^t/(1+t^2), y(0) = 1, y'(0) = 0.

(b) Solve the separable differential
equation
y'=
(7e^-3x+2x^2-xcosx)/-6y^3
(c) Solve the IVP
x(1-siny)dy=(cosx-cosy-y)dx
.
y(π/2)=0

Solve Differential equation by variation of parameters method.
y"-5y'+6y=e^x

ﬁnd the general solution of the given differential equation
1. y''−2y'+2y=0
2. y''+6y'+13y=0
ﬁnd the solution of the given initial value problem
1. y''+4y=0, y(0) =0, y'(0) =1
2. y''−2y'+5y=0, y(π/2) =0, y'(π/2) =2
use the method of reduction of order to ﬁnd a second solution of
the given differential equation.
1. t^2 y''+3ty'+y=0, t > 0; y1(t) =t^−1

Solve the following 2nd Order differential equation and find
y(x):
y'' + 2y' +y = x + e-x
y(0) = 0, y'(0) = 0.

solve the given differential equation (x^2) y’’ -6y=0
please explain step by step

Solve the differential equation by variation of parameters. y''
+ 3y' + 2y = 1/(4+e^x)

Solve the differential equation write the answer without
fractions and negative exponents :
(6y+x^2y^11) dx - (x^3y^10-6x) dy = 0

Solve the differential equation
(1-y)dx-x^2y^2dy=0

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