Internal problem ID [11691]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _Bernoulli]
\[ \boxed {{\mathrm e}^{2 x} y^{2}+{\mathrm e}^{2 x} y y^{\prime }=2 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 24
dsolve([(exp(2*x)*y(x)^2-2*x)+(exp(2*x)*y(x))*diff(y(x),x)=0,y(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \sqrt {2}\, \sqrt {{\mathrm e}^{2 x} \left (x^{2}+2\right )} \]
✓ Solution by Mathematica
Time used: 0.337 (sec). Leaf size: 25
DSolve[{(Exp[2*x]*y[x]^2-2*x)+(Exp[2*x]*y[x])*y'[x]==0,{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {2} e^{-x} \sqrt {x^2+2} \]