Internal problem ID [13062]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.3 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right )-\sin \left (\frac {y}{x}\right )=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(cos(y(x)/x)*(diff(y(x),x)-y(x)/x)=1+sin(y(x)/x),y(x), singsol=all)
\[ y = \arcsin \left (c_{1} x -1\right ) x \]
✓ Solution by Mathematica
Time used: 60.351 (sec). Leaf size: 185
DSolve[Cos[y[x]/x]*(y'[x]-y[x]/x)==1+Sin[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\pi x}{2} y(x)\to \frac {3 \pi x}{2} y(x)\to -2 x \arccos \left (\frac {1}{2} \left (e^{\frac {c_1}{2}} \sqrt {x}-\sqrt {2-e^{c_1} x}\right )\right ) y(x)\to 2 x \arccos \left (\frac {1}{2} \left (e^{\frac {c_1}{2}} \sqrt {x}-\sqrt {2-e^{c_1} x}\right )\right ) y(x)\to -2 x \arccos \left (\frac {1}{2} \left (e^{\frac {c_1}{2}} \sqrt {x}+\sqrt {2-e^{c_1} x}\right )\right ) y(x)\to 2 x \arccos \left (\frac {1}{2} \left (e^{\frac {c_1}{2}} \sqrt {x}+\sqrt {2-e^{c_1} x}\right )\right ) \end{align*}