Solve the exact differential equation. (e^y + x^2 + sin(y)) dx + x(e^y + cos(y)) dy = 0

Question.

Solve the exact differential equation.

(e^y + x² + sin(y)) dx + x(e^y + cos(y)) dy = 0

Solution:

Solve the IVP (2xy + x^4)dx + (x^2 + y^2)dy =0 y(0)=1

Question.

Solve the IVP

(2xy + x⁴)dx + (x² + y²)dy =0

y(0)=1

Solve the following exact differential equation. ( 6xye^(2y) + 4x^3 ) dx + ( 3x^2 e^(2y) + 6x^2 ye^(2y) - 2sin(2y) ) dy = 0

Question.

Solve the following exact differential equation.

( 6xye^2y + 4x³ ) dx + ( 3x²e^2y + 6x²ye^2y - 2sin(2y) ) dy = 0

Solution:

Check if the following differential equation is exact? If so, solve. (4e^x sin(y) - 2y)dx + (-2x + 4e^x cos(y))dy = 0

Question.

Check if the following differential equation is exact? If so, solve.

(4e^x sin(y) - 2y)dx + (-2x + 4e^x cos(y))dy = 0

Solution:

Solve the initial value problem (2x + e^y)dx + xe^y dy = 0, y(1) = 0

Question.

Solve the initial value problem (2x + e^y)dx + xe^y dy = 0, y(1) = 0

Solution:

dy/dx = (-2x^3 - 2y)/(6x - y^4)

Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose level curves are solutions to the differential equation dy/dx = (-2x^3 - 2y)/(6x - y^4)