40.2.24 problem 49

Internal problem ID [6602]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 49
Date solved : Monday, January 27, 2025 at 02:15:28 PM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y^{2}+y x -x y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 22

dsolve([(y(x)^2+x*y(x))-x*diff(y(x),x)= 0,y(1) = 1],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x}}{\operatorname {Ei}_{1}\left (-x \right )+{\mathrm e}-\operatorname {Ei}_{1}\left (-1\right )} \]

✓ Solution by Mathematica

Time used: 0.156 (sec). Leaf size: 19

DSolve[{(y[x]^2+x*y[x])-x*D[y[x],x]== 0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x}{-\operatorname {ExpIntegralEi}(x)+\operatorname {ExpIntegralEi}(1)+e} \]