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List of top Mathematics Questions on Partial Differential Equations
If $(x/a)^n + (y/b)^n = 2$, then $dy/dx$ at $(a,b)$ is
AP ECET Metallurgical Eng - 2026
AP ECET Metallurgical Eng
Mathematics
Partial Differential Equations
The solution of $\frac{\partial^2 z}{\partial x^2} + z = 0$, satisfying $z(0,y) = e^y$, $\left(\frac{\partial z}{\partial x}\right)_{x=0} = 1$ is $z(x,y) = $}
TS PGECET - 2026
TS PGECET
Mathematics
Partial Differential Equations
If $z = x^2 y + e^{xy^2}$, then $\left(\frac{\partial^2 z}{\partial x^2} + \frac{\partial^2 z}{\partial x \partial y}\right)$ evaluated at $(1,0)$ is:}
TS PGECET - 2026
TS PGECET
Mathematics
Partial Differential Equations
The differential equation \[ 2\frac{\partial^2 z}{\partial x^2} + 5\frac{\partial^2 z}{\partial x\partial y} + 2\frac{\partial^2 z}{\partial y^2} + 7\frac{\partial z}{\partial x} + \frac{\partial z}{\partial y} =0 \] is classified as
TS PGECET - 2026
TS PGECET
Mathematics
Partial Differential Equations
The general solution of the linear partial differential equation (PDE): \(x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=z\) is ____ (\(\phi\) is an arbitrary function).
CPET - 2025
CPET
Mathematics
Partial Differential Equations
In solving the heat equation using separation of variables, the eigenvalues correspond to ____.
CPET - 2025
CPET
Mathematics
Partial Differential Equations
Which of the following statements is/are true for the PDE: \((1+x^2)u_{xx}+(1+y^2)u_{yy}+xu_x+yu_y=0\)?
(I) It is classified as parabolic PDE.
(II) The canonical equation is \(u_{\xi\xi}+u_{\eta\eta}=0\).
CPET - 2025
CPET
Mathematics
Partial Differential Equations
Solution of the PDE \(u_x+yu_y=0\) with the initial condition \(u(0,y)=y^3\) is ____.
CPET - 2025
CPET
Mathematics
Partial Differential Equations
A string of length 1 meter is fixed at both ends and obeys the wave equation \(u_{tt}=4u_{xx}\) with initial conditions: \(u(x,0)=\sin(\pi x)\), \(u_t(x,0)=0\). Then its solution \(u(x,t)\) is ____.
CPET - 2025
CPET
Mathematics
Partial Differential Equations
If \(u = e^{xy}\), then the value of \(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\) at (1, 1) is
AP ECET CE - 2025
AP ECET CE
AP ECET CSE - 2025
AP ECET CSE
Mathematics
Partial Differential Equations
If \(z = x^2 - y^2\) then \( \frac{1}{x} \frac{\partial z}{\partial x} + \frac{1}{y} \frac{\partial z}{\partial y} = \)
AP ECET CE - 2025
AP ECET CE
AP ECET CSE - 2025
AP ECET CSE
Mathematics
Partial Differential Equations
Particular integral of $f(D)y = \cos ax$ is
AP ECET ME - 2025
AP ECET ME
AP ECET ECE - 2025
AP ECET ECE
AP ECET Metallurgical Eng - 2025
AP ECET Metallurgical Eng
AP ECET Mining Engg - 2025
AP ECET Mining Engg
Mathematics
Partial Differential Equations
Complementary function of the differential equation $(D^3 - 8)y = x$ is
AP ECET ME - 2025
AP ECET ME
AP ECET ECE - 2025
AP ECET ECE
AP ECET Metallurgical Eng - 2025
AP ECET Metallurgical Eng
AP ECET Mining Engg - 2025
AP ECET Mining Engg
Mathematics
Partial Differential Equations
Particular integral of $f(D)y = \cos ax$ is
AP ECET EIE - 2025
AP ECET EIE
Mathematics
Partial Differential Equations
Complementary function of the differential equation $(D^3 - 8)y = x$ is
AP ECET EIE - 2025
AP ECET EIE
Mathematics
Partial Differential Equations