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Popular >

(d^5-d)y=2x+2^x

Solution

(d^{5} - d) y = 2 x + 2^{x}

Solution

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + c_{4} cos (x) + c_{5} sin (x) + e^{x} \cdot \int \frac{e ^{- x} ( 2 x + 2 ^{x} )}{4} d x + \frac{- 4 ln ^{3} ( 2 ) ln ( 2 e ) x ^{2} - 4 ln ( 2 ) ln ( 2 e ) x ^{2} + 2 ln ^{3} ( 2 ) ln ( 2 e ) x + 2 ln ( 2 ) ln ( 2 e ) x + ln ^{3} ( 2 ) \cdot 2 ^{x} + ln ( 2 ) \cdot 2 ^{x} - ln ^{2} ( 2 ) ln ( 2 e ) \cdot 2 ^{x + 2} - ln ( 2 e ) \cdot 2 ^{x + 2} + ln ^{2} ( 2 ) ln ( 2 e ) \cdot 2 ^{x + 1} + 2 ln ^{3} ( 2 ) ln ( 2 e ) + 2 ln ( 2 ) ln ( 2 e )}{4 ln ^{3} ( 2 ) ln ( 2 e ) + 4 ln ( 2 ) ln ( 2 e )}

Solution steps

(d^{5} - d) y = 2 x + 2^{x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + c_{4} cos (x) + c_{5} sin (x) + e^{x} \cdot \int \frac{e ^{- x} ( 2 x + 2 ^{x} )}{4} d x + \frac{- 4 ln ^{3} ( 2 ) ln ( 2 e ) x ^{2} - 4 ln ( 2 ) ln ( 2 e ) x ^{2} + 2 ln ^{3} ( 2 ) ln ( 2 e ) x + 2 ln ( 2 ) ln ( 2 e ) x + ln ^{3} ( 2 ) \cdot 2 ^{x} + ln ( 2 ) \cdot 2 ^{x} - ln ^{2} ( 2 ) ln ( 2 e ) \cdot 2 ^{x + 2} - ln ( 2 e ) \cdot 2 ^{x + 2} + ln ^{2} ( 2 ) ln ( 2 e ) \cdot 2 ^{x + 1} + 2 ln ^{3} ( 2 ) ln ( 2 e ) + 2 ln ( 2 ) ln ( 2 e )}{4 ln ^{3} ( 2 ) ln ( 2 e ) + 4 ln ( 2 ) ln ( 2 e )}

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + c_{4} cos (x) + c_{5} sin (x) + e^{x} \cdot \int \frac{e ^{- x} ( 2 x + 2 ^{x} )}{4} d x + \frac{- 4 ln ^{3} ( 2 ) ln ( 2 e ) x ^{2} - 4 ln ( 2 ) ln ( 2 e ) x ^{2} + 2 ln ^{3} ( 2 ) ln ( 2 e ) x + 2 ln ( 2 ) ln ( 2 e ) x + ln ^{3} ( 2 ) \cdot 2 ^{x} + ln ( 2 ) \cdot 2 ^{x} - ln ^{2} ( 2 ) ln ( 2 e ) \cdot 2 ^{x + 2} - ln ( 2 e ) \cdot 2 ^{x + 2} + ln ^{2} ( 2 ) ln ( 2 e ) \cdot 2 ^{x + 1} + 2 ln ^{3} ( 2 ) ln ( 2 e ) + 2 ln ( 2 ) ln ( 2 e )}{4 ln ^{3} ( 2 ) ln ( 2 e ) + 4 ln ( 2 ) ln ( 2 e )}

Popular Examples

(d^3+3d^2+2d)y=x^2

(d^{3} + 3 d^{2} + 2 d) y = x^{2}

(d^2-2d+1)*y=x*e^x*cos(x)

(d^{2} - 2 d + 1) \cdot y = x \cdot e^{x} \cdot cos (x)

d^{2} (d^{2} + 1) y = 1

y^{'''}+3y^{''}=-36x^2+12x+42

y^{^{'''}} + 3 y^{^{''}} = - 36 x^{2} + 12 x + 42

y^{''}-y^'=e^{2x}*cos(e^x)

y^{^{''}} - y^{^{'}} = e^{2 x} \cdot cos (e^{x})

Frequently Asked Questions (FAQ)

What is the solution for (d^5-d)y=2x+2^x ?
The solution for (d^5-d)y=2x+2^x is