83.39.4 problem 4

Internal problem ID [19472]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (D) at page 135
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:45:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y&=\left (1+x \right ) {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 21

dsolve((x+2)*diff(y(x),x$2)-(2*x+5)*diff(y(x),x)+2*y(x)=(x+1)*exp(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.994 (sec). Leaf size: 45

DSolve[(x+2)*D[y[x],{x,2}]-(2*x+5)*D[y[x],x]+2*y[x]==(x+1)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -e^x+\frac {c_1 e^{2 x+2}}{\sqrt {2}}-\frac {e^2 c_2 (2 x+5)}{2 \sqrt {2}} \]