Internal problem ID [5259]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {y^{2}+y x -y^{\prime } x=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (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: 0.161 (sec). Leaf size: 19
DSolve[{(y[x]^2+x*y[x])-x*y'[x]== 0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{-\operatorname {ExpIntegralEi}(x)+\operatorname {ExpIntegralEi}(1)+e} \]