29.31.33 problem 934

Internal problem ID [5512]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 934
Date solved : Monday, January 27, 2025 at 11:34:46 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4&=0 \end{align*}

✓ Solution by Maple

Time used: 0.085 (sec). Leaf size: 47

dsolve(x^4*diff(y(x),x)^2+2*x^3*y(x)*diff(y(x),x)-4 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {2 i}{x} \\ y \left (x \right ) &= \frac {2 i}{x} \\ y \left (x \right ) &= \frac {2 \sinh \left (c_{1} -\ln \left (x \right )\right )}{x} \\ y \left (x \right ) &= -\frac {2 \sinh \left (c_{1} -\ln \left (x \right )\right )}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.263 (sec). Leaf size: 71

DSolve[x^4 (D[y[x],x])^2+2 x^3 y[x] D[y[x],x]-4==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {4 e^{c_1}}{x^2}-\frac {e^{-c_1}}{4} \\ y(x)\to \frac {e^{-c_1}}{4}-\frac {4 e^{c_1}}{x^2} \\ y(x)\to -\frac {2 i}{x} \\ y(x)\to \frac {2 i}{x} \\ \end{align*}