Internal problem ID [2806]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 51.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\left (3+x -4 y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 36
dsolve(diff(y(x),x) = (3+x-4*y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x \,{\mathrm e}^{-4 x} c_{1}+7 \,{\mathrm e}^{-4 x} c_{1}-2 x -5}{8 \,{\mathrm e}^{-4 x} c_{1}-8} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 41
DSolve[y'[x]==(3+x-4 y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{16} \left (4 x+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}+10\right ) \\ y(x)\to \frac {1}{8} (2 x+5) \\ \end{align*}