Solve x2 + x + (µ²x² – n²)y = 0, µ # 0,n > 0 dx

Q: dx xt x(1) = 2, solve for x(2) when h = 0.1 %| dt t²+2

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: Obtain the general solution using separation of variables ye 2x dx = (4 + e2x)dy

A: The given differential equation is y e2x dx=4+e2xdy Solving the differential equation by converting…

Q: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

A: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

Q: Reducible to Exact (2xy ln y)dx+(x2+y2√y2+1)dy=0 Have to be convert to exact by integration method

A: Given  Differntial equation (2xy ln y)dx+(x2+y2√y2+1)dy=0

Q: y)dx

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Q: SOLVE USING INTEGRATING FACTOR 4. (4x2 – 4xy + 3y² + 2) dx +x (2x – 2y + 1) dy = 0

A: Given, ∫(4x2-4xy+3y2+2)(-2x2+2xy-x) dx                                     ⇒−∫ 4 x2 + 4 y x − 3 y2−…

Q: 1. S(7x³ + 4x²)dx e*dx 2. J itez* 1+e2x 3. S(V1 – cos x)dx

A: We will these indefinite integrals as

Q: 2. Integrate numerically the given function, fx0.1(1.2-x)(1-e20(x-1)) dx with the multiple-segment…

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Q: What is the general solution of =? %3D dx y2+1 What is the general solution of (y + 1) = 2x? %3D…

A: (As per bartleby guidelines, for questions containing multiple subparts, only three subparts will be…

Q: Solve the initial value prol dy + 8, y(1) = 3 dx y%3D 4 Jx +8x 19 4 Oy=Vx + 8x - 6 Oy=-- - 8x- 6

A: Explanation and solutions is given below....

Q: dx 4-t x(0) = 1, solve for x(0.5) when h = 0.05 %3D dt t+x

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: S2x²e** ax=uv- Jvau -Svau. Sfoxe". Using Integration By Parts, Find uv- Jv du- 3 x² e dx O 2 x3 x3…

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Q: 1 Integrate: dx I V100–49x²

A: Given

Q: 2ydx + x(2 + x²y) dy = 0 %3D

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Q: Find the general solution of the differentlal equation. (Use C for the constant of Integration.) dy…

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Q: Finding a General Solution Using Separation of Variables. dy/dx= (x-1)/y3

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Q: Find a set of solution. Integrating factors found by inspection.   y(x2 + xy2 - 1) dx + x (x2 + y2…

A: Given the differential equation y(x2 + xy2 - 1) dx + x (x2 + y2 +1) dy =0. We need to find the set…

Q: x2 dy dx by reversing the order of integration. 4/x 1. Evaluate

A: Given double integral is∫14 ∫4x4x2 dy dxNow , By interchanging the integral we have ,∫y=14…

Q: Q2: Find the integration by applying substitution method: 7 dX (X - 1)VX- 2x - 48

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Q: 5. = 2y – 1 dx Solution: = = 2y – 1 (Multiply both sides by dx) = dy = (2y– 1)dx (Divide both sides…

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Q: dx 1. dt xt x(0) = 1, solve for x(0.3) when h = 0.1 I| -

A: Given function is, dxdt=-12xt,   x(0)=1, h=0.1 and we need to solve, x(0.3)   Here we have, (t0,…

Q: Solve for the approximate value of (z² + 3z + 6) dx at n = 5. Solve also the true value of the…

A: To approximate the given integral by using trapezoidal rule.

Q: 4. Using homogenous D.E approach, solve (x³ – 3xy?)dx = (y3 – 3x²y)dy.

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Q: 6. Use Methods of Integrating factor to solve the DE below: dz + 2 xz = 2 e-x? a) dx dy b) x 2- 2 y…

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Q: dx 15. S (x²+36) ³/2

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Q: 1.(x fan y t y) dx - xdy = 0 2- ye "dx - (ure)dy cbssitication and Solution by appropiate methed

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Q: (x²y)dx + (x³ + 2y³)dy = 0 ||

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

Q: (b) Find S x+1 dx. [Hint: Rules of integration and Tri 9+x2 Given v2 – 9 Y and v – G

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Q: (b) Evaluate f 3æ“ In6x dx using integration by parts.

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Q: Test for exactness and determine the particular solution of: (yexy – 2y³)dx+ (xexy – 6xy2 – 2y)dy =…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the general solution: k^2 dx+(x-y+k)^2 dy3D0

A: Given that: k2dx+(x-y+k)2dy=0     NOTE: As per our answering guidelines, we can only answer 1…

Q: Solve for the general solution of the given DE by using the integrating factors found by inspection.…

A: Please refer the attached image for complete solution.

Q: 1. Obtain the particular solution when x = 1 and y = 1 5) dx 3 + y 3 dy = 0 y

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Q: Find a positive constant that satisfies the equation: ∫(1/x²+a²)dx=1    integration limits: [ 0,…

A: Consider the equation ∫0∞1x2+a2dx=1 We have to find the value of a Use integral formula…

Q: 4. y? cos x dx + (4 + 5y sin x )dy = 0

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Q: SOLVE USING INTEGRATING FACTOR 5. y(x +2y + 2) dx + (2xy +5) dy = 0 %3D

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Q: 4. S 2z3 el-z dz 5. S Vx In(Vx) dx Vr3 6. Si, Inx dx

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Q: 4. x(x² – y² – x)dx – y(x² – y²)dy = 0, y(2) = 0

A: For the solution follow the next step.

Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: 2. Evaluate the integral. -2 (a) (x² – 3x) dx - -1 •3 (b) Lce L(e + 2)(t – 3) dt -2 (c) 2.9 x° dx

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Q: Integrate ∫x(√4 − x )dx (a) by parts, letting dv =( √4 − ) dx. (b) by substitution, letting u = 4 −…

A: Consider the integrals, ∫x4-xdx…

Q: 4. Using homogenous D.E approach, solve (x³ – Зху?)dx %3D (у3 — 3x2у)dy. (v³ – 3x²y)dy. | 2 (ardai…

A: The given differential equation is; (x3-3xy2)dx=(y3-3x2y)dy.

Q: dr2 dx dx d²y, 7 dy , 9y 3. dr2 dy =1 at x = 1. dx = 0; y = 0 and x dx x2 4. Use the method of…

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Q: Solve using separation of variables xy^2 dx + e^x dy = 0; when x -> infinite, y -> 1/2.

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Q: To integrate x3 ex2 x " 0x we apply integration by parts and in the form u dv, dv is set as:

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Q: A. Integration By Parts 1. ſx5Vx3 + 1 dx 2. S/* x sin 2x dx 3. S- x³ex? -dx (x2+1)2

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Q: What is the appropriate substitution to solve dy/dx + ln(x+1)y/x = x^3y^3? z=y^-2 z=y^2 z=y^3 y=vx

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Evaluate the double integral : 2 2 (3 x² + 4 y°) dx dy Answer: 2 2 (3 x2 + 4 y) dæ dy =

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Q: Trapezoidal (Use n = 9) 3 5. S¹ (5√x-³) dx √x 6. √² (5ex - e)dx

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Q: #7 Integrate using trig substitution o X s dx

A: A detailed solution is given below

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.