60.1.332 problem 333

Internal problem ID [10346]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 333
Date solved : Monday, January 27, 2025 at 07:17:39 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 38

dsolve((2*x^(5/2)*y(x)^(3/2)+x^2*y(x)-x)*diff(y(x),x)-x^(3/2)*y(x)^(5/2)+x*y(x)^2-y(x) = 0,y(x), singsol=all)
 

\[ -\frac {3 \left (\frac {\left (c_{1} +\frac {3 \ln \left (x \right )}{2}-3 \ln \left (y\right )\right ) x^{{3}/{2}} y^{{3}/{2}}}{3}+x y-\frac {1}{3}\right )}{y^{{3}/{2}} x^{{3}/{2}}} = 0 \]

✓ Solution by Mathematica

Time used: 0.298 (sec). Leaf size: 72

DSolve[-y[x] + x*y[x]^2 - x^(3/2)*y[x]^(5/2) + (-x + x^2*y[x] + 2*x^(5/2)*y[x]^(3/2))*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {2 \sqrt {x y(x)} \log (y(x))}{\sqrt {x} \sqrt {y(x)}}-\frac {\sqrt {x y(x)} \left (3 x^{3/2} y(x)^{3/2} \log (x)+6 x y(x)-2\right )}{3 x^2 y(x)^2}=c_1,y(x)\right ] \]