Internal problem ID [4614]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{3 x -2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 15
dsolve([diff(y(x),x)=exp(3*x-2*y(x)),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\ln \relax (3)}{2}+\frac {\ln \left (2 \,{\mathrm e}^{3 x}+1\right )}{2} \]
✓ Solution by Mathematica
Time used: 1.409 (sec). Leaf size: 23
DSolve[{y'[x]==Exp[3*x-2*y[x]],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \log \left (\frac {1}{3} \left (2 e^{3 x}+1\right )\right ) \\ \end{align*}