29.32.4 problem 938

Internal problem ID [5516]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 32
Problem number : 938
Date solved : Monday, January 27, 2025 at 11:34:55 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \end{align*}

✓ Solution by Maple

Time used: 0.304 (sec). Leaf size: 53

dsolve(4*x^5*diff(y(x),x)^2+12*x^4*y(x)*diff(y(x),x)+9 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {1}{x^{{3}/{2}}} \\ y \left (x \right ) &= -\frac {1}{x^{{3}/{2}}} \\ y \left (x \right ) &= \frac {x^{3} c_{1}^{2}+1}{2 x^{3} c_{1}} \\ y \left (x \right ) &= \frac {x^{3}+c_{1}^{2}}{2 x^{3} c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.700 (sec). Leaf size: 75

DSolve[4 x^5 (D[y[x],x])^2+12 x^4 y[x] D[y[x],x]+9==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {x^3 \text {sech}^2\left (\frac {3}{2} (-\log (x)+c_1)\right )}} \\ y(x)\to \frac {1}{\sqrt {x^3 \text {sech}^2\left (\frac {3}{2} (-\log (x)+c_1)\right )}} \\ y(x)\to -\frac {1}{x^{3/2}} \\ y(x)\to \frac {1}{x^{3/2}} \\ \end{align*}