Sr Examen
Ecuación diferencial dx*(x^2+x*y*exp(x^2*y)+cos(2*x))+dy*(x^2*exp(x^2*y)/2+y)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2
2 d x *y(x)
2 x *--(y(x))*e
2 d x *y(x) dx
x + --(y(x))*y(x) + x*e *y(x) + -------------------- + cos(2*x) = 0
dx 2
$$\frac{x^{2} e^{x^{2} y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)}}{2} + x^{2} + x y{\left(x \right)} e^{x^{2} y{\left(x \right)}} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \cos{\left(2 x \right)} = 0$$
x^2*exp(x^2*y)*y'/2 + x^2 + x*y*exp(x^2*y) + y*y' + cos(2*x) = 0
Respuesta
[src]
// 2 \
|| x *y(x) |
||e |
2 3 ||-------- for 2*y(x) != 0|
y (x) sin(2*x) x || 2*y(x) |
----- + -------- + -- + |< |*y(x) = C1
2 2 3 || 2 |
|| x |
|| -- otherwise |
|| 2 |
\\ /
$$\frac{x^{3}}{3} + \left(\begin{cases} \frac{e^{x^{2} y{\left(x \right)}}}{2 y{\left(x \right)}} & \text{for}\: 2 y{\left(x \right)} \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases}\right) y{\left(x \right)} + \frac{y^{2}{\left(x \right)}}{2} + \frac{\sin{\left(2 x \right)}}{2} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.2397960382432236)
(-5.555555555555555, 2.4300004960959596)
(-3.333333333333333, 6.750002692060633)
(-1.1111111111111107, 60.750044346287986)
(1.1111111111111107, 1178944664952232.0)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 1.7159818507571235e+185)
(7.777777777777779, 8.388243571809211e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)