83.8.11 problem 12

Internal problem ID [19137]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 01:05:08 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.203 (sec). Leaf size: 25

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

\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} m +\ln \left (\sec \left (\textit {\_Z} \right )^{2} x^{2}\right )+2 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 34

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

\[ \text {Solve}\left [m \arctan \left (\frac {y(x)}{x}\right )-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=\log (x)+c_1,y(x)\right ] \]