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# Calculus/Euler method for ODE's

Question
How to find excat solution of y'+ y =x + cos x

i am doing euler method but could not find a method to find exact solution of above probelm?plz explain with steps it is first order differental equation.pls note that i have find y using euler method.

dy/dx + y = x + cos(x)

integrating factor is e^∫dx = e^x

multiply both sides by e^x we get

e^x(dy/dx + y) = x * e^x +  e^x * cos(x)

d/dx(y * e^x) = x * e^x +  e^x * cos(x)

ie. y * e^x = ∫ x * e^xdx + ∫  e^x * cos(x)dx.

It is now easy to find y using integration by parts

Calculus

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#### mervyn

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I can solve problems in calculus, advanced calculus, differential and partial differential equations, complex variables, Fourier series and integrals, analysis,Gram-Schmidt orthogonalization, and Legendre polynomials. Soon I will be able to answer any question on advanced engineering control.

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