Internal problem ID [5108]
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: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
\[ \boxed {y+y^{\prime }-y^{4} {\mathrm e}^{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 138
dsolve(diff(y(x),x)+y(x)=y(x)^4*exp(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {2^{\frac {1}{3}} \left ({\mathrm e}^{2 x} \left (2 \,{\mathrm e}^{2 x} c_{1} +3\right )^{2}\right )^{\frac {1}{3}} {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 x} c_{1} +3} \\ y \left (x \right ) &= -\frac {\left (1+i \sqrt {3}\right ) 2^{\frac {1}{3}} \left ({\mathrm e}^{2 x} \left (2 \,{\mathrm e}^{2 x} c_{1} +3\right )^{2}\right )^{\frac {1}{3}} {\mathrm e}^{-x}}{4 \,{\mathrm e}^{2 x} c_{1} +6} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} \left ({\mathrm e}^{2 x} \left (2 \,{\mathrm e}^{2 x} c_{1} +3\right )^{2}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right ) {\mathrm e}^{-x}}{4 \,{\mathrm e}^{2 x} c_{1} +6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.751 (sec). Leaf size: 90
DSolve[y'[x]+y[x]==y[x]^4*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-2}}{\sqrt [3]{e^x \left (3+2 c_1 e^{2 x}\right )}} \\ y(x)\to \frac {1}{\sqrt [3]{\frac {3 e^x}{2}+c_1 e^{3 x}}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{\frac {3 e^x}{2}+c_1 e^{3 x}}} \\ y(x)\to 0 \\ \end{align*}