60.1.227 problem 228

Internal problem ID [10241]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 228
Date solved : Monday, January 27, 2025 at 06:41:04 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62&=0 \end{align*}

✓ Solution by Maple

Time used: 0.665 (sec). Leaf size: 212

dsolve((4*y(x)+11*x-11) *diff(y(x),x)-25*y(x)-8*x+62=0,y(x), singsol=all)
 

\[ y = \frac {4 \left (x +\frac {1}{2}\right ) {\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{{2}/{3}} \left (\sqrt {3}+i\right )-4 i \left (-19 x +7\right ) {\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{{1}/{3}}+64 \left (x +\frac {1}{2}\right ) \left (i-\sqrt {3}\right )}{\sqrt {3}\, {\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{{2}/{3}}-16 \sqrt {3}+i {\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{{2}/{3}}-8 i {\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{{1}/{3}}+16 i} \]

✓ Solution by Mathematica

Time used: 60.189 (sec). Leaf size: 1677

DSolve[(4*y[x]+11*x-11)*D[y[x],x]-25*y[x]-8*x+62==0,y[x],x,IncludeSingularSolutions -> True]
 

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