83.28.2 problem 2

Internal problem ID [19367]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (B) at page 106
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:35:34 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

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

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

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