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Classify the following as true or false give reasons for your answers.
i) For the Initial Value Problem, dy/dx = f(x,y), y(x0)=y0, the continuity of f(x,y) and ∂f/∂y guarantees the unique solution of the problem.
ii) Equations (d2y/dx2) - 2x(dy/dx) + x2y = e(x^2)/2 and d2y/dx2 +y = 1 have the same normal form.
iii) Equation cos(x+y)p + sin(x+y)q = z2 + z is a quasi-linear equation
iv) (∂2z/∂x2)(∂2z/∂y2) - (∂2z/∂x∂y)2 = 0 is a non-linear Partial Differential Equation.
v) Every solution of the Ordinary Differential Equation (D2+1)2y = 0 is bounded on [0,∞[ .
Find the differential equation of the family of curves x2+y2+2ax+2by+c=0, where a, b, c are parameters.
(D2-D'2-3D+3D')z=xy+7
- [(e/√x -2√x) - y/√x] = dy/dx
- xdy/dx +y=x3y6
- dr/dx = tyanchya - r2/coax
- y dx/dy = x-yx2siny
- (x2-4xy-2y2)dx + (y2-4xy-2x2)dy=0
- (x2-xtan2y+sec2y)dy = (tany-2xy-y)dx
- (2xy4ey+2xy3+y)dx + (x2y4ey-x2y2-3x)dy=0
- (y/x secy-tany)dx+(secy logx-x)dy=0
- y dy/dx +4x/3 -y2/3x =0
(D2 - 4) y= xe2 , xex is yp = (ax + b) ex
Three students were given a differential equation y''+π ^2y=0 to solve.
(D2 - 4 ) y = xex
Reduce to canonical form
uxx - uxy + uyy + ux = 0
Reduce to canonical form :
𝑢𝑥𝑥 − 𝑢𝑥𝑦 + 𝑢𝑦𝑦 + 𝑢𝑥 = 0
