29.18.12 problem 488

Internal problem ID [5086]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 488
Date solved : Monday, January 27, 2025 at 10:08:40 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.981 (sec). Leaf size: 212

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

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

✓ Solution by Mathematica

Time used: 60.187 (sec). Leaf size: 1677

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

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