Internal problem ID [2807]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\left (1+4 x +9 y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(diff(y(x),x) = (1+4*x+9*y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {4 x}{9}-\frac {1}{9}-\frac {2 \tan \left (-6 x +6 c_{1}\right )}{27} \]
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 49
DSolve[y'[x]==(1+4 x+9 y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{81} \left (-36 x+\frac {1}{c_1 e^{12 i x}-\frac {i}{12}}-(9+6 i)\right ) \\ y(x)\to \frac {1}{27} (-12 x-(3+2 i)) \\ \end{align*}