Find whether the given ODE is exact or not, in any case find its solution (x2 + y? + 2x)dx – 2ydy = 0

Q: dx Find given that dt 6x² + 7y² = 13 x = 1, y = -1, and Give your answer as a simple fraction. dx dt…

A: Let us consider an expression, ax+by=c , a,b,c are constants. Then by implicit differentiation on…

Q: Q.9 Let (x) be a solution to the equation [exy'] + xy=0, x=(-∞0,00) dx Given that (-¹)=0,…

A: The given equation is ddxexy'+xy=0, x∈-∞,∞. Find the value of ϕx.

Q: (2x+ 3 f) te* )dx t (dg e xyf+ £CW)dy=o find f)+o that makes this equahion exact

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Q: Find the particular solution of the following ODE given that y(0)=0 and y'(0)=3: d'y dy +10 +25y = 0…

A: Explanation of the answer is as follows

Q: T/2 Evaluate I = | sin x dx using Euler-Maclaurin’s formula.

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Q: Solve the following ODE by introducing integrating factor on the process of your calculation: x dy +…

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Q: Find the particular solution of the given ODE. ( y − √x² + y²) dx − xdy = 0 when r = √3, y = 1 - -

A: This is homogeneous ordinary first order nonlinear differential equation

Q: Determine whether the equation is exact. If it is, then solve it. (2xy + 4)dx + (x - 4) dy = 0 For…

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Q: Solve the ODE by finding an integrating factor for exact equations. (2xy2+3x)dx - 2xydy=0

A: Recall: If the equation M(x,y)dx +N(x,y)dy=0 is not exact and ∂M∂y-∂N∂xN is a function of x only…

Q: Solve the following 1st order ODE. x² (3x+-)dx+(²- +32)dy=0 y 6. у

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Q: Find the general solution of the given ODE. (x+y-1)dx - (x + y)dy = 0

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Q: Use separation of variables to find the general solution to the ODE 2,3 x*y° dx +e¬* (y? – y) dy = 0

A: We solve the given differential equation by separating the variables.

Q: Evaluate dz using the given information. z = ln(x2 + y2); x = 2, y = 3, dx = 0.02, dy = -0.03

A: z=ln(x2+y2)x=2;y=3;dx=0.02;dy=-0.03;

Q: Identify the Bernoulli's equation of first order ODE. None of these b. dy -+10x²y=sin x dx C. dy…

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Q: 3. Solve the following linear ODE: dy (a) +2y=3x², y(1)= 3. dx

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Q: Find the general solution of the given ODE ( 40² – v) dx + x dy 0.

A: The given DE is: (y2-y)dx+x dy=0⇒(y2-y)dx=-x…

Q: Find the general solution (y, x, C) = 0 to the following ODE dy x(7 — х — 2у) - у (5 — х — у) dx

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Q: Solve the given ODE: dy :- y = /9x² +y². dx

A: Given: xdydx-y=9x2+y2 For finding solution of given differential equation, first we simplify it So,…

Q: Q3) The solution of ODE * (3yx² -) : dx +(x + cosy + dy = 0 O y^2+2x+C O y+y/x+siny+C O y/x+cos x+C…

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Q: . Solve the following ODE using separable variable method: * +(x+2)y = 0. dx a)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Test for exactness, and solve the Initial Value Problem for the following first-order ODE below: dy…

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Q: Find the Gcneral Solution of the ff.: * u sing Homogen cous, Exact or Non -Ex act Formula. +)…

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Q: 4. Solve the ODE using Separation of Variables. X. dy - y = 2x²y dx

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Q: plem 1: Find the solution of the following initial value problell dy r cos(r) cos(x) y(0) = -1 dx

A: given dydx=xcos(x)y at x=0 , y= -1

Q: Find the particular solution of the following ODE given that y(0)=0 and y '(0)=0: d'y +y=e* dx

A: A Particular solution of the differential equation is a solution of the form y= f(x) , which don't…

Q: A. Find the function f that satisfies the equation / f(1) dt : 2 cos x + 3x – 5. d B. Evaluate: dx 3…

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Q: Evaluate dz using the given information z = ln(x2 + y2); x = 2, y = 3, dx = 0.02, dy = -0.03

A: We have a given function as   z=ln(x2+y2) it is given that x = 2 y = 3 dx = 0.02 dy = -0.03 We…

Q: Show that the given ODE is an Exact Equation and the solve it. (2xy − 6x² + 4y) dx + (x² + 4x + y³ −…

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Q: Choose the value for a such that of 32 x² y cos(ax)dx d y = −4ñª 02 O None of the others O 2 0-2 O…

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Q: (1+ In x) dx + (1+ ln y) dy = 0

A: Here we solve the differential equation

Q: dy e y- e-Y +e-2x-y 1. dx

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Use Euler's method to solve the following ODES wwwwwwww dy dx = -2y + 4e¯*, with h = 0.18 from x = 0…

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Q: dy Solve the ODE: dx 1+ y? Solve the IVP: ty' + (t+ 1)y = t, y(ln 2) = 1, t >0 0

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Q: Find the particular solution of the following ODE given that y(0)=7 and y'(0)=0: d’y dy dx -+3-10y=0…

A: Given differential equation is, d2ydx2+3dydx-10y = 0with initial conditions y(0) = 7; y'(0) = 0

Q: Find the solution to the second order Linear ODE y" - 3y' + 2y = 10 sin %3D X y(0) = 1 and y'(0) =…

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Q: ) Using Huen's method to estimate the solution of the ODE y' = cos (xy?) ,y(1) = 2, h = 0.1 If y1=…

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Q: Q11. For the ODE dy = (y cos(x) + 2x)/y ,y(0) = 0.8 dx %3! The most accurate answer when estimating…

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Q: 9. dy dx (xy + 1)2

A: We have to evaluate the iterated integral given below: ∫01∫01 xxy+12dydx. First we will evaluate the…

Q: d) r- cos r + +3r = 4r3. %3D

A: the given implicit function is: x-cosx2+y2x+3x5=4x3 we have to differentiate the given implicit…

Q: Find the particular solution of the following ODE given that y(0 d’y +y=e* dx

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Q: Find the solution of the following linear ODE given that y(5)=3 dy Зу = (x – 4)² х—4 dx

A: Use integrating factor for the differential equation.

Q: 00 | f(x) cos axdx = S2 – a,0 2

A: Value of f(x)

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

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Q: 1. Test whether the following ODE is an exact DE then solve it. a) arctan(y) dx +y dy = 0 b) (x2 +…

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Q: 1. Separate r and y variable and solve the following ODE: dx y In x- dy y +

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Q: Solve D.E using bernouliis equation r'y-x'. dy x'y-x' . dx = y* · cos(x)

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Q: 2. Determine if the following ODE is exact. If it is exact, find the general solution. If not, find…

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Q: a) Check if the following ODE is exact. If not, find an integrating factor to convert it to an exact…

A: (a) [2x tan(y)]dx + [sec2(y)]dy = 0 (b) y3dx - x[x2+y2]dy = 0;  y(1) = 1

Q: B. (y + e*seny)dx + (x + e*cosy)dy = 0

A: First we will classify the differential equation then find the general solution using the method…

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.