Show that the solution curves of the differential equation y(2x3 – y3) dy x(2y3 – x³) dx are of the form x3 + y³ = Cxy.

Q: dy_ y* +2xy³ – 3x²y² – 2.x³y 2.2 4 dx 2x²y² – 2x³y– 2xr* -

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Q: Calculate the value(s) of C for which y=x'-2C is a solution to the differential equation dy -3y-54 =…

A: We have to find the value of C

Q: Solve the particular solution of the differential equation dy/dx = 4xy< with the initial condition x…

A: Given : dydx=4xy2 ; y(1)=1 is the condition The particular solution is given as follows:

Q: a. if y = asin3x + bcos3x satisfies the differential equation d?y + 4 + 3y = 10cos3x, find a, b. dx2…

A: Now , first  we will find d^2y/ dx^2 and dy/dx Then,  we will find the value of a and b.

Q: Show that the solution of the differential equation (1+y2)dx+(1+x2)dy = 0; y(0) =−1 is xy−x−y−1=0.

A: The given differential equation is:

Q: 1. Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

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Q: Find the solution of the differential equation that satisfies the given initial condition. dy %3D…

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Q: Find the particular solution to the differential equation dy 3x²y + 6x² /ỹ dx with initial condition…

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Q: The complementary function of the differential equation d²y dx² 2 + 3x +y= dy dx 1 is (1-x)²

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Q: Find the order differential equation of ddy] 6 dy dy dy +7. + 6- 3. +7 = 0 dx3 dx2 dx

A: Given that a differential equation and find the order of this differential equation. We know that…

Q: Find a particular solution y, of the differential equation: (a) 2y" + 4y' + 7y = x2 (b) y" + 9y = 2…

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Q: 5. Find the solution of the differential equation that satisfies the given initial condition. dy =y²…

A: Topic- differential equations

Q: dy = 2xV1 – y² dx

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Q: y(3) – 3y" + y' – 3y = e3t + 1

A: Consider the provided D.E, y3-3y''+y'-3y=e3t+1⇒D3-3D2+D-3y=e3t+1 The Auxiliary equation is written…

Q: Find the general solution of the given second-order differential equation. Зу" + 2y' + у %3D 0 y(x)…

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Q: Verify that y = e 3x cos 2x is a solution of the differential equation y"-6y' + 13y = 0

A: To verify that y=e3x cos 2x is a solution of the differential equation y''-6y'+13y=0.

Q: Consider the Non-Homogenous differential equation: y"-2y"-4y' +8y 2xe-2* +x+9 Given that y,-Ce-+ C,e…

A: Consider the Non-Homogenous differential equation:

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: Given first differential equation(y-x)y'=y-x+2To find: y=x+2x+6 is the solution of the given…

Q: The solution of the non-exact differential equation 2ydx + (3y-2x)dy = 0 is (2x/y)+3lny=Dc O…

A: Given  2ydx + (3y - 2x)dy = 0

Q: Find the particular solution of the first-order linear differential equation (3y + 5) cos x dx = dy…

A: Consider the given differential equation 3y+5 cosx dx=dy,    yπ=0

Q: Find a second solution of each differential equation. x²y" + xy' + y = 0; y1 = cos (In x). (1+x)y" +…

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Q: Find the solution of the differential equation (In(y))6 dy dx = x°y which satisfies the initial…

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Q: If xm is a solution of the differential equation x²y" – 2y = 0 then m %3D -

A: Given that a second order differential equation and also given a solution of this equation is xm and…

Q: Find the solution of the differential equation (In(y))³ dy dx = x'y 3 which satisfies the initial…

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Q: Solve the Bernoulli differential equation dy 2 y3 +-y dx X x3

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Q: (6x + y²) dæ + y (2x – 3 ) dy = 0 is a variable separable differential equation. -

A: Variable separable differential equation is any differential equation that can be written in the…

Q: Find the general solution of the first-order differential equation                        x dx + ( y…

A: Consider the following differential equation: xdx+y+eyx2+1dy=0y+eyx2+1dy=-xdxy+eydy=-xx2+1dx…

Q: Determine the particular solution of the given differential equation y(x2 + y2) dx + x(3x2 - 5y2)…

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Q: Verify that y = c, sin 3x + c2 cos 3x + 4e* is a solution to the differential equation y"-y" + 3y'-…

A: We have to verify that, y = c_1 sin 3x + c_2 cos 3x + 4e^x ;  is a solution to the differential…

Q: Find a solution to the differential equation dy 4x3 dx ey which satisfies the initial condition y(0)…

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Q: Solve the Cauchy-Euler differential equation d'y dy +2x-20y xr + 2x +1 dx dx

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Q: (군2-1) 을 + 2y3 (+ 1)°

A: Given ODE : (x2-1)dydx+2y=(x+1)2 ⇒dydx+2yx2-1=(x+1)2x2-1⇒dydx+2yx2-1=x+1x-1 Which Linear…

Q: Find the solution of the differential equation that satisfies the given initial condition. Y = (8x +…

A: To solve the given differential equation.

Q: Verify that y1 = x and y2 = xe" are solutions of the differential equation x²yll – x(x + 2)y! + (x +…

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Q: Find the solution of the following second order differential equation d²y(x) dy +x- +x² y(x) = 0 dx…

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Q: The solution of the non-exact differential equation 2ydx + (3y- 2x)dy = 0 is O (2y/x)+Iny=c O…

A: topic - differential equations

Q: Find the solution of the differential equation that satisfies the given initial condition. x +…

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Q: Find a particular solution y, of the differential equation: 2y" + 4y' + 7y = x2

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Q: Discretize the differential equation y" + y' + 4ty = (t – (})), y'(0) = 2, y'(3) = -2 with step-size…

A: Given the differential equation y"+y'+4ty=δt-32, y'0=2, y'3=-2, h=34. We will be using the following…

Q: Consider the Non-Homogenous differential equation: y"-2y"-4y' +8y = 2xe-2x +x+9 %3D Given that y, =…

A: Given that      The non-homogenous differential equation       y"'-2y"-4y'+8y = 2xe-2x+x+9 Also…

Q: Find the solution of the differential equation that satisfies the given initial condition. dy = (8x…

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Q: Find the general solution of the first-order linear differential equation. dy 2y dx x > 0 y =

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Q: Find the solution to the differential equation (x2 + 1)y'' + 2xy' + 2y = (x2 + 1)2 with the…

A: Given, Using the Green's function method. If are independent solutions of the homogeneous part of…

Q: Consider the Non-Homogenous differential equation: y" + 2y' = xe-5* + 3x² - 2 Given that y, C, +…

A: Given non homogenous differential equation and also given complementary function is given.  We have…

Q: Verify that the function c,(x + y)° = xek is a solution of the differential equation (x² + y² }kdx…

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Q: (1 + In xy) dx + (1 + x/y) dy = O

A: The given exact differential equation is…

Q: dx x2-y2-xy 0 ху dy

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Q: Verify that y = e3x cos 2x is a solution of the differential equation y"-6y +13y = 0.

A: We have to show that y is the solution of given differential equation

Q: x²dx + y(1 – x)dy = 0

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Q: Verify that the indicated relation is an implicit solution of the given first order differential…

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