- solve; dy A: dx e* * y3 x+1

Q: Solve the diff eq. (Homogenous) dy dx + x²(y² + 3) y(x³ + 1)

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Q: Solve the DE dy 2xy-y2 dx x2

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Q: S16 -X2 メー dy dx + x?+yz

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Q: solve. (exy + e²) dx + (zey + e*) dy + (ey −exy - e'z) dz

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

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

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: Find the particular solution of dy/dx=6e^3x+1,andf(0)=0.

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Q: Solve y? dx + (x Vy² – x² – xy) dy = 0 - -

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Q: 2. xy'dx + e"dy = 0

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Q: Solve the linear D.E dy = (e-X sec2x - y)dx

A: Given: dy=e-xsec2x-ydx ⇒dydx=e-xsec2x-y⇒dydx+y=e-xsec2x which is linear differential equation of the…

Q: Find dy/dx if : Y =x(x/a) + √ a2 - x2

A: Given: To Find:

Q: 4. Solve dx -dy = 0 %3D x²y xy?

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Q: Find dy/dx If y ex A 2/א"e ],/איe D-2V B.

A: We have to find dy/dx.

Q: Q2) Solve the D.E dy – (2x/1- y²)dx = %3D

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Q: d²y dy y = e * is a solution of dx2 = 0 dx

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Q: Obtain the general solution. d²y e* 1. dx? dy 2 +y= dx x² +1

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Q: Solve equatian. the differentiql dy = 80-2y * Such that y=70 when x=0

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Q: Solve the DE (3xy² – y³)dx +(xy² – 2x²y)dy = 0 %3D

A: Given equation is, ...(1) Let, be the dependent variable then divide by we get, Now, substitute…

Q: : x d²y dy dx² dx + +my = 0, given that

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Q: Find the constant m if y = emx satisfies dx2 d²y 5 + 6y = 0 dx

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Q: Find d2y/dx2 implicitly in terms of x and y.

A: To findd2ydx2

Q: Solve the D.E x dy+ (2y-x-11dメ-0 (24-X-1)dxメ= 0 %3D

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Q: Solve the D.E dy + (xy – xy²)dx = 0 %3D

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Q: Solve th D.E using Exact (6x² – y +3)dx+(3y – x – 2)dy

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Q: Solve the Euler equation d²y dy -x +y= dx dx (In x-1)

A: Solution

Q: find the dy さ× when 3In X リ=(メ+z)m

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Q: I Solve the fllowing FODF 2y(x+y+2) dx + (y²-x²_ 4x-1)dy = o when x=2,y= 3

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Q: Solve the Linear DE: 2y (y2 - x) dy = dx. %3D

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Q: Find the general solution of  dy/dx + y/x= 3/y

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Q: Solve the D.E dy – (2x/1- y2)dx = 0

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Q: Solve the D.E. x² + y² dx = 2x dx + 2y dy %3D

A: Arrange the differential equation as

Q: dy e2x -3 Find if y = In %3D dx 1-4x

A: SOLUTION-

Q: Solve: (r* + y") dy = xy dx

A: we have to solve the given differential equation . (x2+y2)dy=xydx

Q: What is the solution? dy/dx - y/x =xy^2

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Q: Find an implicit general solution of ( x² + dx + 1+ 4x²y², - y*) dy = 0 %3D 1+4x²y?

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Q: Solve the D.E dy -(2x /1-y2)dx = 0

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Q: Find the complete solution of d2y/dx2 +2dy/dx+y =sinxcos2x.

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Q: Solve this IVP. dy 7 + 2y = x, y(0) = dx

A: Linear Ordinary Differential Equation with Constant Coefficients: The general form of linear…

Q: [" In(y+z) e dxdzdy = [Show your solution.]

A: Given that,

Q: x In y dy dx -1J

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Q: Solve the DE. (1+x²)dy + [(1-x)²-xe^-x]dx = 0; when x = 0, y = −2

A: This is a problem of ordinary differential equation. first of all we will simplify it into dy/dx…

Q: Find dy If y=1-t and x2 dx

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Q: find d^2y/dx^2 implicitly in terms of y and x  2y^3=3x^4

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Q: Find the Particular Solution: y(x - 6y)dx - x(2x - 9y)dy = 0 ; when x=1, y=1

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Q: Solve: 3(1 + t?)(dy/dt) = 2ty(y³ - 1). %3D

A: Solve the integral 31+t2dydt=2tyy3-1. Use the separation of variable method. 1yy3-1y'…

Q: Find, the, general solution of 2 dy + y = xe"Inx. dx²

A: Given the differential equation           y''-2y'+y=xexlnx Find the general solution.

Q: dy ycotx + y³cscx dx

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Q: Obtain the general solution to the equation. dx 8 y: + 4x = 9y dy

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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.