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]]
\[ \boxed {\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y=\left (x +1\right )^{3} {\mathrm e}^{x}} \] 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 \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 22
dsolve([(1+x)^2*diff(diff(y(x),x),x)-2*(1+x)*diff(y(x),x)-(x^2+2*x-1)*y(x) = (1+x)^3*exp(x), (1+x)*exp(x), y(0) = 1, D(y)(0) = -1], singsol=all)
\[ y \left (x \right ) = \frac {\left (x +1\right ) \left (x \,{\mathrm e}^{x}-5 \sinh \left (x \right )+2 \cosh \left (x \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 21.262 (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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