60.2.342 problem 919

Internal problem ID [10929]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 919
Date solved : Monday, January 27, 2025 at 10:25:13 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

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

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 191

dsolve(diff(y(x),x) = y(x)^(3/2)*(x-y(x)+y(x)^(1/2))/(y(x)^(3/2)*x-y(x)^(5/2)+y(x)^2+x^3-3*x^2*y(x)+3*x*y(x)^2-y(x)^3),y(x), singsol=all)
 

\[ -\frac {\left (c_{1} x^{6}+80 x^{3}-54 x^{2}-12 x -1\right ) y^{{7}/{2}}+\left (-6 c_{1} x^{5}-60 x^{2}+36 x +6\right ) y^{{9}/{2}}+\left (15 c_{1} x^{4}+24 x -9\right ) y^{{11}/{2}}+\left (-60 x^{4}+36 x^{3}+6 x^{2}\right ) y^{{5}/{2}}+\left (-20 c_{1} x^{3}-4\right ) y^{{13}/{2}}+\left (24 x^{5}-9 x^{4}\right ) y^{{3}/{2}}+15 y^{{15}/{2}} c_{1} x^{2}-6 y^{{17}/{2}} c_{1} x +y^{{19}/{2}} c_{1} -4 x^{6} \sqrt {y}+12 y \left (y^{2}+\left (-2 x -\frac {1}{3}\right ) y+x^{2}\right ) \left (x -y\right )^{3}}{y^{{7}/{2}} \left (x -y\right )^{6}} = 0 \]

✓ Solution by Mathematica

Time used: 45.039 (sec). Leaf size: 251

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

\[ y(x)\to \text {Root}\left [\text {$\#$1}^9 c_1{}^4-6 \text {$\#$1}^8 c_1{}^4 x+\text {$\#$1}^7 \left (15 c_1{}^4 x^2-6 c_1{}^2\right )+\text {$\#$1}^6 \left (-20 c_1{}^4 x^3+30 c_1{}^2 x-4+2 c_1{}^2\right )+\text {$\#$1}^5 \left (15 c_1{}^4 x^4-60 c_1{}^2 x^2+24 x-6 c_1{}^2 x+9\right )+\text {$\#$1}^4 \left (-6 c_1{}^4 x^5+60 c_1{}^2 x^3-60 x^2+6 c_1{}^2 x^2-36 x-6\right )+\text {$\#$1}^3 \left (c_1{}^4 x^6-30 c_1{}^2 x^4+80 x^3-2 c_1{}^2 x^3+54 x^2+12 x+1\right )+\text {$\#$1}^2 \left (6 c_1{}^2 x^5-60 x^4-36 x^3-6 x^2\right )+\text {$\#$1} \left (24 x^5+9 x^4\right )-4 x^6\&,1\right ] \]