83.8.27 problem 28

Internal problem ID [19153]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 01:10:05 PM
CAS classification : [_Bernoulli]

\begin{align*} y \left (2 y x +{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

dsolve(y(x)*(2*x*y(x)+exp(x))-exp(x)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.296 (sec). Leaf size: 25

DSolve[y[x]*(2*x*y[x]+Exp[x])-Exp[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {e^x}{x^2-c_1} \\ y(x)\to 0 \\ \end{align*}