B. EXACT EQUATIONS Find the general solution of the following differential eqo (1) (x2 +y2) + 2xy dy + 2xy = 0 dx (2) 3y sin x 2xy cos x = 0 dy (3) 3x²y² + 2x³y =

Q: Given y(x) = c₁e²x + c₂e* + 2 sinx, find the values for ₁ and ₂ so that the conditions y(0) = 0 and…

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Q: y' = y tan x – y² sec x

A: a. The given problem is                        y'=ytanx-y2secx ; x∈0,π2

Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

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Q: Solve (sin(x) cos(y)) dx + (cos(x) sin(y))dy = 0 if possible. If the equation is not exact, say so.…

A: First we check given differential equation is exact or not.  If given differential equation is exact…

Q: x*cos(y/x)*dy/dx = y*cos(y/x)-x   find solution of that differantial equation.

A: Let us consider the differential equation of the form dydx=fyx  then to solve the differential…

Q: r(t) = (3√2t, e³t, e-3t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). 3√2e³x +…

A: Question (1) (a) We need to find the unit tangent and unit normal vector T(t) and N(t) of the vector…

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

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Q: B) Find the general solution of the equation by using (Undetermined Coefficients method) d'y dy de =…

A: Solution of the differential equation using undetermined method

Q: Solve the differential equation y + (tanx) y=cosx ? Ay=xsinx+Csinx By=xsinx+Ccos.x Ⓒy=sinx+Ccos.x D…

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Q: h45. Solve for the general solution of y'= sinx + ycotx a. y = (x+ C)sinx b. y = Cxsinx c. y = (x +…

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Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: 3-(cos x)y' =yCv-1) sin x.

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Q: y" – 2y" + 3y' = x² + cos3x

A: Answer

Q: Use variation of parameters to find a particular solution, given the solutions y₁, y2 of the…

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Q: 1.) (1+x) dy -y dx=0 2.) dy dx 3y =6

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Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y"-81y'…

A: Sol:- y'''-81y'=te-9t+10cos9tFirst , find the yh:-yh is the solution to the homogeneous ODE…

Q: Equation y" - 2y + 2y = exsinx (5) (21 2 2 Appropriate Form of the Particular Solution

A: We need to solve Differential equation. As per Bartleby guidelines we can solve one question from…

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b.…

A: Separable equation:   A first order differential equation y’ = f (x, y) is called a separable…

Q: 4. Get the exact a. dy = cos 2x dz differentials of y = (sin 2)² b. dy=sin 2z dz dy = sin 2x d.…

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Q: Solve  y′ + 2y cos(2t) = 2 cos(2t), y(π/2 ) = 0

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Q: [(cos 2y) – 3x?y²] dx + [(cos 2y) – 2x(sin 2y) – 2x³y] dy = 0 %3D

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Q: Find the general solution of the equation: y" - y' - 6y = exp(-x) - 7 cos x %3D

A: We find the general solution of  y"-y'-6y=e-x-7cos(x).....(1)

Q: y′′ + 16y = 32 cos(4x) − 24 sin(4x)

A: The given differential equation is        y'' + 16y = 32cos(4x) − 24sin(4x)…

Q: Question 2 Find the solution to the DE. (y-x+xycotx) dx + xdy=0 xysinx=C+ sinx - xcosx Oy=(c +…

A: Concept: For a differential equation of the form P(x,y)dx+Q(x,y)dy=0 The differential equation is…

Q: Q2: Find General Solution (YGS)to the equation (Yª-1) Y=COS(2x)

A: From the given information. The given differential equation is as follows.

Q: Find the solution. (D³ +7D2 + 19D + 13)y =0; when x =0, y=0. y' =2, y"=-12 A y = e-2'sin3x B y =…

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Q: Find the solution. dy sin x x +2y = y(2) = 1 dx , X A y = (4 + sin 2 + cosx²)/x² (B) cy= (3 cos 2x -…

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