29.4.12 problem 101

Internal problem ID [4703]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 101
Date solved : Monday, January 27, 2025 at 09:32:28 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }+x^{3}&=x \sqrt {x^{4}+4 y} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 47

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

\[ \frac {\left (y \left (x \right )-c_{1} \right ) \sqrt {x^{4}+4 y \left (x \right )}-x^{2} \left (c_{1} +y \left (x \right )\right )}{x^{2}+\sqrt {x^{4}+4 y \left (x \right )}} = 0 \]

✓ Solution by Mathematica

Time used: 1.786 (sec). Leaf size: 68

DSolve[D[y[x],x]+x^3==x Sqrt[x^4+4 y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to (\cosh (2 c_1)+\sinh (2 c_1)) \left (-x^2+\cosh (2 c_1)+\sinh (2 c_1)\right ) \\ y(x)\to (\cosh (2 c_1)+\sinh (2 c_1)) \left (x^2+\cosh (2 c_1)+\sinh (2 c_1)\right ) \\ y(x)\to 0 \\ \end{align*}