Internal problem ID [4666]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 8. Special second order equations. Lesson 35. Independent variable x
absent
Problem number: Exercise 35.16, page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {\left (1+y\right ) y^{\prime \prime }-3 {y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = -{\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 15
dsolve([(y(x)+1)*diff(y(x),x$2)=3*(diff(y(x),x))^2,y(1) = 0, D(y)(1) = -1/2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {-x +\sqrt {x}}{x} \]
✓ Solution by Mathematica
Time used: 1.693 (sec). Leaf size: 572
DSolve[{(y[x]+1)*y''[x]==3*(y'[x])^2,{y[1]==0,y'[0]==-1/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {6 \left (\left (-12+3\ 2^{2/3} \sqrt [3]{27-3 \sqrt {69}}-\sqrt [3]{2} \left (27-3 \sqrt {69}\right )^{2/3}+3\ 2^{2/3} \sqrt [3]{3 \left (9+\sqrt {69}\right )}-\sqrt [3]{2} \left (3 \left (9+\sqrt {69}\right )\right )^{2/3}\right ) x+3 \sqrt {2} \sqrt {\left (12-3\ 2^{2/3} \sqrt [3]{27-3 \sqrt {69}}+\sqrt [3]{2} \left (27-3 \sqrt {69}\right )^{2/3}-3\ 2^{2/3} \sqrt [3]{3 \left (9+\sqrt {69}\right )}+\sqrt [3]{2} \left (3 \left (9+\sqrt {69}\right )\right )^{2/3}\right ) x-\sqrt [3]{2} \left (3 \left (9+\sqrt {69}\right )\right )^{2/3}+2\ 2^{2/3} \sqrt [3]{3 \left (9+\sqrt {69}\right )}+\sqrt [3]{9-\sqrt {69}} \left (9+\sqrt {69}\right )^{2/3}+\left (9-\sqrt {69}\right )^{2/3} \sqrt [3]{9+\sqrt {69}}-\sqrt [3]{2} \left (27-3 \sqrt {69}\right )^{2/3}+2\ 2^{2/3} \sqrt [3]{27-3 \sqrt {69}}+6}+\sqrt [3]{2} \left (3 \left (9+\sqrt {69}\right )\right )^{2/3}-2\ 2^{2/3} \sqrt [3]{3 \left (9+\sqrt {69}\right )}-\sqrt [3]{9-\sqrt {69}} \left (9+\sqrt {69}\right )^{2/3}-\left (9-\sqrt {69}\right )^{2/3} \sqrt [3]{9+\sqrt {69}}+\sqrt [3]{2} \left (27-3 \sqrt {69}\right )^{2/3}-2\ 2^{2/3} \sqrt [3]{27-3 \sqrt {69}}-6\right )}{\left (12-3\ 2^{2/3} \sqrt [3]{27-3 \sqrt {69}}+\sqrt [3]{2} \left (27-3 \sqrt {69}\right )^{2/3}-3\ 2^{2/3} \sqrt [3]{3 \left (9+\sqrt {69}\right )}+\sqrt [3]{2} \left (3 \left (9+\sqrt {69}\right )\right )^{2/3}\right ) \left (6 x+2^{2/3} \sqrt [3]{3} \left (\sqrt [3]{9-\sqrt {69}}+\sqrt [3]{9+\sqrt {69}}\right )\right )} \]