Internal problem ID [11658]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {{\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([exp(x)*(y(x)-3*(exp(x)+1)^2)+(exp(x)+1)*diff(y(x),x)=0,y(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}+1 \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 12
DSolve[{Exp[x]*(y[x]-3*(Exp[x]+1)^2)+(Exp[x]+1)*y'[x]==0,{y[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (e^x+1\right )^2 \]