Solve the PDE ∂z/∂x + ∂z/∂y = z2
∂z∂x+∂z∂y=z2The auxillairy equation are, dx=dy=dzz2Integrate the first two fractions. We have that; x=y+ax−y=aIntegrate the last two fractions y=−1z+by+1z=b.Hence the solution is f(a,b)=f(x−y,y+1z)=0.\frac{\partial z}{\partial x}+\frac{\partial z}{\partial y}=z^2\\ \text{The auxillairy equation are, }\\ dx=dy=\frac{dz}{z^2}\\ \text{Integrate the first two fractions. We have that; }\\ x=y+a\\ x-y=a\\ \text{Integrate the last two fractions }\\ y=-\frac{1}{z}+b\\ y+\frac{1}{z}=b.\\ \text{Hence the solution is } f(a,b)=f(x-y,y+\frac{1}{z})=0.∂x∂z+∂y∂z=z2The auxillairy equation are, dx=dy=z2dzIntegrate the first two fractions. We have that; x=y+ax−y=aIntegrate the last two fractions y=−z1+by+z1=b.Hence the solution is f(a,b)=f(x−y,y+z1)=0.
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Dear Anand, please use the panel for submitting new questions.
The product of two divergent sequences is divergent. True or false? Justify.
Comments
Dear Anand, please use the panel for submitting new questions.
The product of two divergent sequences is divergent. True or false? Justify.