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Popular >

y^{'''}-ay^'=1+cosh(ax)

Solution

y^{^{'''}} - a y^{^{'}} = 1 + cosh (a x)

Solution

y = c_{1} + c_{2} e^{a x} + c_{3} e^{- a x} - \frac{a x + sinh ( a x )}{a ^{2}} + e^{a x} \cdot \int \frac{e ^{- a x} ( cosh ( a x ) + 1 )}{2 a} d x + e^{- a x} \cdot \int \frac{e ^{a x} ( cosh ( a x ) + 1 )}{2 a} d x

Solution steps

y^{'''} (x) - a y^{'} (x) = 1 + cosh (a x)

Solve linear ODE:

y = c_{1} + c_{2} e^{a x} + c_{3} e^{- a x} - \frac{a x + sinh ( a x )}{a ^{2}} + e^{a x} \cdot \int \frac{e ^{- a x} ( cosh ( a x ) + 1 )}{2 a} d x + e^{- a x} \cdot \int \frac{e ^{a x} ( cosh ( a x ) + 1 )}{2 a} d x

y = c_{1} + c_{2} e^{a x} + c_{3} e^{- a x} - \frac{a x + sinh ( a x )}{a ^{2}} + e^{a x} \cdot \int \frac{e ^{- a x} ( cosh ( a x ) + 1 )}{2 a} d x + e^{- a x} \cdot \int \frac{e ^{a x} ( cosh ( a x ) + 1 )}{2 a} d x

Popular Examples

y^{''}+5y^'+8y=24+23x+12x^2

y^{^{''}} + 5 y^{^{'}} + 8 y = 24 + 23 x + 12 x^{2}

4y^{''}-y=1,y^'(0)= 1/2

4 y^{^{''}} - y = 1, y^{^{'}} (0) = \frac{1}{2}

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

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

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

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

y^{''}-6y^'+9y=t^2e^3

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{2} e^{3}

Frequently Asked Questions (FAQ)

What is the solution for y^{'''}-ay^'=1+cosh(ax) ?
The solution for y^{'''}-ay^'=1+cosh(ax) is