6. The slope field for the differential equation dy x²y + y2 4x + 2y dx will be undefined (have vertical segments) when (A) y = 2x, only (B) y = -2x, only (C) y = -x², only (D) y = 0, only (E) y = 0 or y = -x² %3D %3D

Q: 33. Compute the differential equation * + y = 0 when y (0) = 1, y (0) = -1 dx2 O y = 3e* - 2xe* O y…

A: Solution

Q: The solution of the differential equation 3.9 + x² + x²y+ 3.9y 1+ Y dy dx using variable separable y…

A: The given equation is dydx=3.9+x2+x2y+3.9y1+y On simplifying this, we get…

Q: 4. Find the linear, nonhomogeneous differential equation with constant coefficients whose solution…

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

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Q: 4. Find the linear, nonhomogeneous differential equation with constant coefficients whose solution…

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Q: 2xydx = (x2 + y²)dy ;y(0) = -1 Ans: y(y + 1) = x²

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Q: A tank with capacity 1000 L initially contains 500L of water and 100 kg of dissolved salt. At t 0, a…

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Q: What is the particular solution to the differential equation (1-xy)? + (y² + (1-xy)- )dy = 0 and y =…

A: Givendx1-xy2 + y2 + x21-xy2dy = 0withy(4) = 1

Q: 7: The point xois a singular point of the differential equation y"+ P(x)y' + Q(x)y = 0 if alytic at…

A: The point x0 is a singular point of the differential equation y''+P(x)y'+Q(x)y=0. Then we have t…

Q: (2) The particular solution y,(x) to the differential equation y" + 100y = sec2 (10x) is of the %3D…

A: Given y"+100y=Sec2(10x) ---1Compairing with y"+q(x)y'+r(x)y=g(x).Auxilliary equation corresponding…

Q: 14. What is the particular solution of the linear differential equation y' = x° - 2xy; when x = 1, y…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

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

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Q: What is the particular solution to the differential equation x(x³ – xy² + 2y³)dy – y(x³ + 2y³)dx = 0…

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Q: 2. The differential equation (4x'y'-6x'y-2r-3)dr +(2x*y-2x' ty = 0 is exact because aN

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Q: 9. What is the general solution for the differential equation y"" - 3y' - 2y = 3x? A. y C₁x +…

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Q: 7. In the differential equation 4(3x+ y-2)dx-(3x+y)dy=0, we let the substitution dw =- (Note: We use…

A:

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

A: Note the following chain rule of differentiation : For a differentiable function y=1f(x)  , y' =…

Q: 2. (a) Check that the first order differential equation 4x- dx dy - 4y =9(/xy² ) is homogeneous and…

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Q: 1 xdy – y(1+ y cos 2x)dx = 0 ;y(0): Ans: 2x + y sin 2x = 0 2

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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: 6.2 What is a differential equation, y depending on x, whose general solution is the function 21…

A: Explanation of the answer is as follows

Q: (6) Show that the solution of the differential equation dr 3 + dy 3(y + 1) is r (y + 1)³ + c y +1 y…

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

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Q: 27. The particular solution of the differential equation x^2 dx - (y+1) dy = 0 if at x=1, y=0 is -…

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Q: 19. The particular solution of the differential equation x^2 dx - (y+1) dy = 0 if y(0)=1 is - O 3y^2…

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Q: 2. In the differential equation (x – 4y –9)dx+(4x+ y – 2)dy = 0 , the lines x- 4x + y- 2=0 intersect…

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Q: 17. What is the general solution of the differential equation (y² + 9)dx + (3x – 2xry)dy = 0? 2y A)…

A: We have to find the general solution of the differential equation y2+9dx+(3x-2xy)dy=0.

Q: 4 (a) Identify the homogeneity of the following second order differential equation and state the…

A: Given second order differential equation  3d2ydx2+5y=2y''+1 A second order differential equation…

Q: 3. The differential equation 3y(r -1dx+(x' +8y-3xdy 0; is exact because ам ON

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Q: The following initial value problem is defined with an exact differential equation. If the solution…

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Q: If y(t) is the solution of the differential equation: y" - 3y' + 2y = e-2t where y'(0) = 1, y(0) =…

A: Laplace transform convert the real variables in to complex variables. The Laplace transforms of…

Q: 4) Match the graph of the particular solution curve to the differential equation. (а) у" — Зу' — 4у…

A: First we calculate the general solution then match with given graphs.

Q: What is the particular solution to the differential equation x(x³ – xy² + 2y³)dy – y(x³ + 2y³)dx = 0…

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Q: Q3. Second order non-homogeneous ordinary differential equation is given as: y"+ y' – 2y = x² - x+e*

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Q: y=Aexp(Bx)+Fexp(Gx) is the particular solution of the second order linear differential equation:…

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Q: x(1+ y³)dy + ydx = 0 ;y(1) = 1 Ans: In(xy)3 + y3 = 1

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

A: To verify that the function y=x+2√x+5 is a solution the given differential equation.

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

A:

Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

A: Solved below

Q: 7. In the differential equation 4(3x+ y-2)dx-(3x+ y)dy=0, we let the substitution dw =- (Note: We…

A: Given differential equation is 4(3x + y - 2)dx - (3x + y)dy = 0

Q: What is the general solution to the the differential equationy'''=0? A y=C₁+C₁₂x 1 By=C₁+C₁₂x+C₁₂x²…

A:

Q: 7. The general solution of the differential equation x^2 dx - (y+1) dy = 0 is O zy^2 + 3y - 6x^3 = C…

A: Topic:- application of integration  Note:- as per our guideline if more than one question uploaded…

Q: 19, 4. 6. Given that the differential equation xy" + xy'- y = 0 has a solution yı=x. Use the

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Q: 12) Consider the differential equation y" + a1(x)y' + ao(x)y = 9 sin(7x) And suppose that Y1 = x Y2…

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Q: 5. The differential equation (3r*e" - 2xktx+(r°e' -sin y}dy = 0 is exact because ƏN ƏM ôx

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

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Q: 12) Consider the differential equation y" + a1(x)y' + ao(x)y = 9 sin(7x) And suppose that Y1 = x Y2…

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Q: 11) Consider the linear differential equation y" – ly = 2e6z + 3x + 8 If the particular solution has…

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Q: The following initial value problem is defined with an exact differential equation. If the solution…

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Q: The General solution of the differential equation 3x2 + 2x + 6 is x3 + x2 + 6x dy using variable…

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