9.33 problem 33

Internal problem ID [1139]

Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number: 33.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y-\left (x +1\right )^{3} {\mathrm e}^{x}=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= \left (x +1\right ) {\mathrm e}^{x} \end {align*}

With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1] \end {align*}

Solution by Maple

Time used: 0.027 (sec). Leaf size: 22

dsolve([(x+1)^2*diff(diff(y(x),x),x)-2*(x+1)*diff(y(x),x)-(x^2+2*x-1)*y(x) = (x+1)^3*exp(x), (x+1)*exp(x), y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {\left (x +1\right ) \left (x \,{\mathrm e}^{x}-5 \sinh \relax (x )+2 \cosh \relax (x )\right )}{2} \]

Solution by Mathematica

Time used: 10.646 (sec). Leaf size: 5749

DSolve[(x+1)^2*y''[x]-2*(x+1)*x*y'[x]-(x^2+2*x-1)*y[x]==(x+1)^3*Exp[x],{y[0]==1,y'[0]==-1},y[x],x,IncludeSingularSolutions -> True]
 

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