29.2.26 problem 51

Internal problem ID [4659]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 51
Date solved : Monday, January 27, 2025 at 09:29:50 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (3+x -4 y\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 32

dsolve(diff(y(x),x) = (3+x-4*y(x))^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} \left (5+2 x \right ) {\mathrm e}^{4 x}-2 x -7}{8 \,{\mathrm e}^{4 x} c_{1} -8} \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 41

DSolve[D[y[x],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*}