Solve the initial value problem dy y = 5e" + 28e5* dx with y(0) = 8.

Q: Solve dy/dx=ax+by+c

A: We need to use substitution method to convert it into separable form

Q: (y^3 - x^3) dy = (3y•(x^2) +1) dx Solve exact diff eq

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Q: 4. Solve dx -dy = 0 %3D x²y xy?

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Q: Solve of the following Clairaut equation y=((x+4)y')+(y')^2

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Q: Solve for C in the solution for dx/dy = xy^3/(2y^4+x^4) ; y(2)=4 Use 2 decimal places

A: Here we have to solve the given differential equation

Q: Solve the equation xy^3 dx + (y + 1)e^(-x) dy = 0.

A: Given:  xy3dx+(y+1)e-xdy=0xy3dx+(y+1)e-xdy=0(y+1)e-xdy=-xy3dxDividing equation on both sides by…

Q: + ¹² = 4t, where y'(1) = 1 and y(1)=2. 4) Solve y" +

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Q: Find y'. y=(4x-4)(2x+1) OA. 16x-2 B. 8x-4 OC. 16x-12 OD. 16x-4

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Q: Find y'

A: given

Q: Solve the Bernoulli's equation dy/dx −1/2(1+ 1/ x)y = (3 /x)y^3

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Q: (1+e' )dx +e" (1-)dy = 0 y

A: To find the solution of the below differential equation.

Q: Find the solution. dy x+5y=2x?y+ dx

A: We have to solve the given differential equation.

Q: f y=y(x) is the desired solution of 2 = f(x,y), Derive Euler %3D teration formula for solving ODES…

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Q: Solve the following equation dy/dx + 2xy + xy^4 = 0

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Q: Solve the homogenous equation (y +(x^2 + y^2)^1/2)dx−xdy = 0

A: According to the given information, it is required to solve the given homogeneous differential…

Q: reduce to linear form and solve the following equation y'+(1/2x)y=x/(y^3)  y(1)=2

A: The given differential equation is: y'+12xy=xy3  …1,   y1=2 This is Bernoulli's equation,so (1) can…

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2

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Q: Solve x³y"+6x²y"+4xy' = 0.

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Q: dy/dx=x+2y-5/x-3y+2

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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.