83.43.11 problem Ex 12 page 14

Internal problem ID [19519]
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 II. Equations of first order and first degree
Problem number : Ex 12 page 14
Date solved : Tuesday, January 28, 2025 at 01:48:12 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 17

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

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