60.1.541 problem 544

Internal problem ID [10555]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 544
Date solved : Monday, January 27, 2025 at 09:02:36 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.973 (sec). Leaf size: 4598

dsolve(x^7*y(x)^2*diff(y(x),x)^3-(3*x^6*y(x)^3-1)*diff(y(x),x)^2+3*x^5*y(x)^4*diff(y(x),x)-x^4*y(x)^5=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {2^{{2}/{3}}}{3 x^{2}} \\ y &= -\frac {2^{{2}/{3}} \left (1+i \sqrt {3}\right )}{6 x^{2}} \\ y &= \frac {2^{{2}/{3}} \left (i \sqrt {3}-1\right )}{6 x^{2}} \\ y &= 0 \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.075 (sec). Leaf size: 80

DSolve[-(x^4*y[x]^5) + 3*x^5*y[x]^4*D[y[x],x] - (-1 + 3*x^6*y[x]^3)*D[y[x],x]^2 + x^7*y[x]^2*D[y[x],x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sqrt [3]{c_1 x^3+c_1{}^{2/3}} \\ y(x)\to 0 \\ y(x)\to \frac {(-2)^{2/3}}{3 x^2} \\ y(x)\to \frac {2^{2/3}}{3 x^2} \\ y(x)\to -\frac {\sqrt [3]{-1} 2^{2/3}}{3 x^2} \\ \end{align*}