29.12.17 problem 336

Internal problem ID [4936]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 336
Date solved : Monday, January 27, 2025 at 09:52:43 AM
CAS classification : [_linear]

\begin{align*} 2 \left (x^{2}+x +1\right ) y^{\prime }&=1+8 x^{2}-\left (1+2 x \right ) y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(2*(x^2+x+1)*diff(y(x),x) = 1+8*x^2-(1+2*x)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = 2 x -3+\frac {c_{1}}{\sqrt {x^{2}+x +1}} \]

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 23

DSolve[2(1+x+x^2)D[y[x],x]==1+8 x^2-(1+2 x)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{\sqrt {x^2+x+1}}+2 x-3 \]