83.49.19 problem Ex 19 page 134

Internal problem ID [19632]
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 19 page 134
Date solved : Tuesday, January 28, 2025 at 02:05:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 27

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

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