12.10.32 problem 32

Internal problem ID [1836]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number : 32
Date solved : Monday, January 27, 2025 at 05:36:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (1+x \right ) y&=\left (x -1\right )^{3} {\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 19

dsolve([(x-1)^2*diff(y(x),x$2)-(x^2-1)*diff(y(x),x)+(x+1)*y(x)=(x-1)^3*exp(x),y(0) = 4, D(y)(0) = -6],y(x), singsol=all)
 

\[ y = x^{2} {\mathrm e}^{x}-{\mathrm e}^{x}-5 x +5 \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 18

DSolve[{(x-1)^2*D[y[x],{x,2}]-(x^2-1)*D[y[x],x]+(x+1)*y[x]==(x-1)^3*Exp[x],{y[0]==4,Derivative[1][y][0] ==-6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x-1) \left (e^x (x+1)-5\right ) \]