Solve the following exact equations, implicit general solutions will suffice: a) (2xy+x^2)dx + (x^2+y^2+1)dy ?= 0       b) x^5 + y^5dy/dx= 0 c)  e^x + y^3+ 3xy^2dy/dx = 0           d) (x+y)cos(x) + sin(x) + sin(x)y′? = 0

Q: Example 4: Solve iv) y" + y = sin2x.

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Q: A) 2xe-x(x + 2) 30) u(1) = 2, u '(1) = -7, v(1) = 7, v '(1) = -3. d at x = 1 dx u B) 2xe-X(2-x)…

A:

Q: 11) 2e(2 sin 7x) sec 7x dx

A: Here is the solution:

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: العنوان solve b sin ² (3x) cos² (5x) dx 2 8 tan³x dx >

A: First, we need to identify the type of integral we are dealing with. The first integral is a product…

Q: d (x2+2x)(sin(x)+5) 7. Find: dx Зx+2

A: To find:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 2 sin² x+1 cos? x +1.

A:

Q: Find (21) (22) if = 5 (cos 75° + i sin 75°) 22 = 5 (cos 35° + i sin 35°) Answer: Z1 = (2₁) (2₂) =…

A:

Q: 1) - 3dx 2) (2-3x)² dx 3) x sin (2x2 - 1) dx (2x-3)2 4) sin3x cos² 3x dx

A: Step 1:Step 2: Step 3: Step 4:

Q: Solve the following equations: 1) y" + y = secx 2) y" + 3y' + 2y 1 1+ex 3) y" + 3y+ 2y = sine*

A: The differential equation is :

Q: dy Find if y = 4 sin?(3x) dx

A: Here we have to find the derivative of function y which is given as above. Here I am attaching a…

Q: 2) y = sin(3x²ex)

A: Find the derivative