29.2.27 problem 52

Internal problem ID [4660]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 52
Date solved : Monday, January 27, 2025 at 09:29:55 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (1+4 x +9 y\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

dsolve(diff(y(x),x) = (1+4*x+9*y(x))^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {4 x}{9}-\frac {1}{9}-\frac {2 \tan \left (-6 x +6 c_{1} \right )}{27} \]

✓ Solution by Mathematica

Time used: 0.173 (sec). Leaf size: 49

DSolve[D[y[x],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*}