Solve the following exact differential equation (etx + 2xy) dx + (cosy+ 2x²y) dy = 0 %3D

Q: 2.5 (x-9)dx +xdy=0 2.

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Q: Solve the following differential equation: (3x°y+2xy)dx+(x'+x +2y)dy 0

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Q: c. y' - y cos t = cos t %|

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Q: 8. Solve the differential equation (x+y)² dy = a². dx

A: Let x+y=t This implies 1+dydx=dtdx

Q: If interest in a bank account is compounded continuously, the amount grows at a rate that is…

A: Solution: Given data, Initial amount P = $1000 rate r= 5% = 0.05 According to continuously…

Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: dx - x = (-²/cost) x³ dt 2t 2

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Q: C1. (a) Solve the nonlinear differential equation x'y-x = v" cos x dx %3D

A: That's easy. Have a great day!!!

Q: 1. *= 2x(1– y)?

A: Solve the differential equation:  dydx=2x1-y2dy1-y2=2xdx∫dy1-y2=∫2xdx11-y=x2+C

Q: Use an appropriate substitution to solve the differential equation (y - xeos² (2)) d. dx - x dy = 0.

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Q: d2y/dx2 + 5 (dy/dx) + 6y = 10 cos x  What is the complementary function of this differential…

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Q: 4 dz = (4x²y + x²)dx + (²x³ — y²)dy = 0

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.