Question

Y*dy=(10sinx-5x^3)dx

Answer 1

Відповідь:

y^2= -20cosx-2.5x^4+C

Пояснення:

у*dy=(10sinx-5x^3)dx

Возьмем интеграл обеих сторон

∫у*dy=∫(10sinx-5x^3)dx

1/2у^2=-10cosx-5/4x^4+C

y^2= -20cosx-2.5x^4+C

Answer 2

To solve the differential equation:

Y*dy = (10sin(x) - 5x^3)dx

You can follow these steps:

1. Separate the variables by moving all terms involving y to the left side and terms involving x to the right side:

Y*dy = 10sin(x)dx - 5x^3dx

2. Integrate both sides:

∫Y*dy = ∫(10sin(x) - 5x^3)dx

3. Integrate the left side with respect to y and the right side with respect to x:

∫Y dy = 10∫sin(x) dx - 5∫x^3 dx

4. Integrate each term individually:

∫Y dy = -10cos(x) - (5/4)x^4 + C

Where C is the constant of integration.

5. Now, you have the equation:

Y = -10cos(x) - (5/4)x^4 + C

This is the general solution to the differential equation. If you have initial conditions or boundary conditions, you can use them to determine the value of the constant C and find the particular solution that satisfies those conditions.