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Popular >

y^{''}-y=c^x+2c^{2x}

Solution

y^{^{''}} - y = c^{x} + 2 c^{2 x}

Solution

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x} ( c ^{x} + 2 c ^{2 x} )}{2} d x + e^{- x} (- \frac{( ec ) ^{x}}{2 ln ( ec )} - \frac{c ^{\frac{x ( 1 + 2 l n ( c ) )}{l n ( c )}}}{1 + 2 ln ( c )})

Solution steps

y^{''} (x) - y = c^{x} + 2 c^{2 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x} ( c ^{x} + 2 c ^{2 x} )}{2} d x + e^{- x} (- \frac{( ec ) ^{x}}{2 ln ( ec )} - \frac{c ^{\frac{x ( 1 + 2 l n ( c ) )}{l n ( c )}}}{1 + 2 ln ( c )})

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x} ( c ^{x} + 2 c ^{2 x} )}{2} d x + e^{- x} (- \frac{( ec ) ^{x}}{2 ln ( ec )} - \frac{c ^{\frac{x ( 1 + 2 l n ( c ) )}{l n ( c )}}}{1 + 2 ln ( c )})

Popular Examples

y^{''}-4y^'+4y=xe^{2x}+x^3e^{2x}

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

y^{''}-11y^'+10y=2x^2-44x+4

y^{^{''}} - 11 y^{^{'}} + 10 y = 2 x^{2} - 44 x + 4

y^{''}+9y=11sec^2(3t)

y^{^{''}} + 9 y = 11 sec^{2} (3 t)

y^{''}-y^'=ex(10+x^2)

y^{^{''}} - y^{^{'}} = e x (10 + x^{2})

y^{''}+9y= 1/9 sin(x)

y^{^{''}} + 9 y = \frac{1}{9} sin (x)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-y=c^x+2c^{2x} ?
The solution for y^{''}-y=c^x+2c^{2x} is