83.49.22 problem Ex 22 page 138

Internal problem ID [19635]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 22 page 138
Date solved : Tuesday, January 28, 2025 at 02:05:47 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{2} {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

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

\[ y = \frac {{\mathrm e}^{x} \left (x -1\right )+c_2 \,x^{2}+c_1}{x} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 25

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

\[ y(x)\to \frac {c_2 x^2+e^x (x-1)+c_1}{x} \]