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Popular >

y^{'''}-3y^{''}-y^'+3y=1+e^x

Solution

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = 1 + e^{x}

Solution

y = c_{1} e^{3 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{3} - \frac{e ^{x} x}{4}

Solution steps

y^{'''} (x) - 3 y^{''} (x) - y^{'} (x) + 3 y = 1 + e^{x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{3} - \frac{e ^{x} x}{4}

y = c_{1} e^{3 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{3} - \frac{e ^{x} x}{4}

Graph

Popular Examples

y^{''}-y=2e^{-t},y(0)=0,y^'(0)=0

y^{^{''}} - y = 2 e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

y^{''}+25y=6sin(5x)

y^{^{''}} + 25 y = 6 sin (5 x)

2y^{''}+3y^'-2y=10x^2-4x-15

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 4 x - 15

x^{'''}+10x^{''}+33x^'+36x=4te^{-3t}

x^{^{'''}} + 10 x^{^{''}} + 33 x^{^{'}} + 36 x = 4 t e^{- 3 t}

y^{''}-6y^'+9y=12e^tsin(t)

y^{^{''}} - 6 y^{^{'}} + 9 y = 12 e^{t} sin (t)

Frequently Asked Questions (FAQ)

What is the solution for y^{'''}-3y^{''}-y^'+3y=1+e^x ?
The solution for y^{'''}-3y^{''}-y^'+3y=1+e^x is y=c_{1}e^{3x}+c_{2}e^{-x}+c_{3}e^x+1/3-(e^xx)/4