81.3.18 problem 18

Internal problem ID [18636]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 12:05:09 PM
CAS classification : [_exact, _rational]

\begin{align*} x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 43

dsolve((x^3-3*x^2*y(x)+5*x*y(x)^2-7*y(x)^3) +(y(x)^4+2*y(x)^2-x^3+5*x^2*y(x)-21*x*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \frac {y \left (x \right )^{5}}{5}+\frac {\left (-21 x +2\right ) y \left (x \right )^{3}}{3}+\frac {5 x^{2} y \left (x \right )^{2}}{2}-x^{3} y \left (x \right )+\frac {x^{4}}{4}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 23.689 (sec). Leaf size: 246

DSolve[(x^3-3*x^2*y[x]+5*x*y[x]^2-7*y[x]^3) +(y[x]^4+2*y[x]^2-x^3+5*x^2*y[x]-21*x*y[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {Root}\left [12 \text {$\#$1}^5+\text {$\#$1}^3 (40-420 x)+150 \text {$\#$1}^2 x^2-60 \text {$\#$1} x^3+15 x^4+60 c_1\&,1\right ] \\ y(x)\to \text {Root}\left [12 \text {$\#$1}^5+\text {$\#$1}^3 (40-420 x)+150 \text {$\#$1}^2 x^2-60 \text {$\#$1} x^3+15 x^4+60 c_1\&,2\right ] \\ y(x)\to \text {Root}\left [12 \text {$\#$1}^5+\text {$\#$1}^3 (40-420 x)+150 \text {$\#$1}^2 x^2-60 \text {$\#$1} x^3+15 x^4+60 c_1\&,3\right ] \\ y(x)\to \text {Root}\left [12 \text {$\#$1}^5+\text {$\#$1}^3 (40-420 x)+150 \text {$\#$1}^2 x^2-60 \text {$\#$1} x^3+15 x^4+60 c_1\&,4\right ] \\ y(x)\to \text {Root}\left [12 \text {$\#$1}^5+\text {$\#$1}^3 (40-420 x)+150 \text {$\#$1}^2 x^2-60 \text {$\#$1} x^3+15 x^4+60 c_1\&,5\right ] \\ \end{align*}