83.41.15 problem 5 (ii)

Internal problem ID [19495]
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 at end of chapter VIII. Page 141
Problem number : 5 (ii)
Date solved : Tuesday, January 28, 2025 at 01:46:42 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 19

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

\[ y \left (x \right ) = {\mathrm e}^{2 x}+\left (c_{1} x^{3}+c_{2} \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.103 (sec). Leaf size: 28

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

\[ y(x)\to \frac {1}{3} e^x \left (c_2 x^3+3 e^x+3 c_1\right ) \]