15.3.10 problem 10

Internal problem ID [2903]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 10
Date solved : Monday, January 27, 2025 at 06:28:09 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +2 y+2&=\left (2 x +y-1\right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.367 (sec). Leaf size: 210

dsolve((x+2*y(x)+2)=(2*x+y(x)-1)*diff(y(x),x),y(x), singsol=all)
 

\[ y = \frac {\left (x -3\right ) {\left (486 \sqrt {\left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_1 \right ) c_1 \left (x -\frac {4}{3}\right )^{2}}+1-486 \left (x -\frac {4}{3}\right )^{2} c_1 \right )}^{{2}/{3}} \left (\sqrt {3}+i\right )-10 i \left (1-x \right ) {\left (486 \sqrt {\left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_1 \right ) c_1 \left (x -\frac {4}{3}\right )^{2}}+1-486 \left (x -\frac {4}{3}\right )^{2} c_1 \right )}^{{1}/{3}}+\left (x -3\right ) \left (i-\sqrt {3}\right )}{{\left (486 \sqrt {\left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_1 \right ) c_1 \left (x -\frac {4}{3}\right )^{2}}+1-486 \left (x -\frac {4}{3}\right )^{2} c_1 \right )}^{{2}/{3}} \sqrt {3}-\sqrt {3}+i {\left (486 \sqrt {\left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_1 \right ) c_1 \left (x -\frac {4}{3}\right )^{2}}+1-486 \left (x -\frac {4}{3}\right )^{2} c_1 \right )}^{{2}/{3}}-2 i {\left (486 \sqrt {\left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_1 \right ) c_1 \left (x -\frac {4}{3}\right )^{2}}+1-486 \left (x -\frac {4}{3}\right )^{2} c_1 \right )}^{{1}/{3}}+i} \]

✓ Solution by Mathematica

Time used: 60.203 (sec). Leaf size: 1687

DSolve[(x+2*y[x]+2)==(2*x+y[x]-1)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

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