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Popular >

y^{'''}-3y^{''}+3y^'-y=x-5e^x

Solution

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 5 e^{x}

Solution

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} - x - 3 - \frac{5 e ^{x} x ^{3}}{6}

Solution steps

y^{'''} (x) - 3 y^{''} (x) + 3 y^{'} (x) - y = x - 5 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} - x - 3 - \frac{5 e ^{x} x ^{3}}{6}

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} - x - 3 - \frac{5 e ^{x} x ^{3}}{6}

Graph

Popular Examples

y^{''}-10y+25=0

y^{^{''}} - 10 y + 25 = 0

y^{''}-6y^'+9y= 1/(x^2)e^{3x}

y^{^{''}} - 6 y^{^{'}} + 9 y = \frac{1}{x ^{2}} e^{3 x}

y^{''}-2y^'+y=(15e^t)/(1+t^2)

y^{^{''}} - 2 y^{^{'}} + y = \frac{15 e ^{t}}{1 + t ^{2}}

x^{''}+4x^'+29=0,x(0)=5,x^'(0)=5

x^{^{''}} + 4 x^{^{'}} + 29 = 0, x (0) = 5, x^{^{'}} (0) = 5

y^{''}-4y^'+3y=3e^{-2t}

y^{^{''}} - 4 y^{^{'}} + 3 y = 3 e^{- 2 t}

Frequently Asked Questions (FAQ)

What is the solution for y^{'''}-3y^{''}+3y^'-y=x-5e^x ?
The solution for y^{'''}-3y^{''}+3y^'-y=x-5e^x is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x-x-3-(5e^xx^3)/6