Find the solution to the initial value problem dy 6xy + y2 + (3x2 + 2xy + 2y) dx =0 y(1) = 3 OA x+y + 2xy2 + y2 + x = 31 OB. 6xy + 2y2 + x = 37 3x²y + 2x2y + x3 + 2x2 + 2y = 24 OD 3x2y + xy2 + y2 = 27 ОЕ xºy + x2y2 + y2 + x = 22
ho Question 1 Solve the separable DE. dy zy dx = dạy2 + x2 + 3y2 +3 »(+4) *+1) = 20+C y2 +1 In = 26 +0 y? + In 26 In (*+1) ==+0
Solve the following differential equations (a) dy – (1 – x2)(1+y?) (b) (2xy + 1) + (x2 + 3y2) dy = 0 (c) com + 4y= 22
Answer is E 7. Find the solution to the initial value problem dy da 6ry2(3ar2 + 2xy + 2y) 0 y(1) 3 A. 6ry2y2x = 37 B. ry y2 +x = 22 C. 3r2y2+ x3 + 2r2 + 2y = 21 D. y2ry y2 + x = 31 E. 3x2yxy2 y? = 27
(2xy - y2 + 2) dx + (x2 – 2xy – 3) dy=0 (Exact Equation)
a) Solve the IVP: (x + y)2dx + (2xy + x2 - 1)dy = 0 ; y(1) = 1 b) Find a continuous solution satisfying the given De subject to initial condition. dy + 2x y = f(x), f(x) = fx, 05x<1 y(0) = 2 dx 10, 821 c) Solve the Bernoulli's equation xy' + y = x²y2
2. Solve the differential equation (2xy + y)dx + (x2 + 3.ry2 – 2y)dy = 0. Answer: x²y + xy3 – y2 = C.
Which one is the solution to this equation e-Ydx - (2y + xe dy = 0 denkleminin çözümü aşağıdakilerden hangisidir? xy - Inx = 0 A) x + y = Cx2 B) y ln x + x2 = 0 xe y - y² =c OD) x2 + (tan y)2 = 0 Ο Ε)
Use the method for solving homogeneous equations to solve the following differential equation 5(x2 + y2) dx + 2xy dy = 0 Ignoring lost solutions, if any, an implicit solution in the form FXy) = C is W = C where (Type an expression using X andy as the variables.) is an arbitrary constant
QUESTION 2 Calculate and simplify det if f(x,y) = O x2 - y2 + 2xy (x2 + y2)2 O 4x(+- x² + 3y2) (x² + y²)3 o 4x(x² – 3y?) (x² + y²)3 OO O x2 - y2 + 2xy (x² + y²)?