query: equation $u_x+u=e^{2y+x}$ (part of the solution to $u_x+u_y+u=e^{x+2y}$)
positive_passages.docid: 25730
positive_passages.text: Solve $u_x + u_y + u = e^{x+2y}$
negative_passages.docid: 14576
negative_passages.text: $(U\cap W)^0 = U^0 + W^0$
negative_passages.docid: 62161
negative_passages.text: Solutions of the Pell-type equation $x^2-2y^2=-1$
negative_passages.docid: 27809
negative_passages.text: Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
negative_passages.docid: 119407
negative_passages.text: Solution of Vector equation
negative_passages.docid: 49073
negative_passages.text: how to obtain solution for $u_t+u=u_{xx}$
negative_passages.docid: 20491
negative_passages.text: How to solve this equation $x^{2}=2^{x}$?
negative_passages.docid: 27611
negative_passages.text: How to solve the differential equation: $yy'^2-2xy'+y=0$
negative_passages.docid: 143765
negative_passages.text: To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$
negative_passages.docid: 144841
negative_passages.text: Find general solution $y''y^3=1$
negative_passages.docid: 12102
negative_passages.text: particular solution to $y^{(4)} -2y'' +y = xe^x $ using undetermined coefficients
negative_passages.docid: 79212
negative_passages.text: Find the general solution of $y'= a^{x + y}$ where y is the function
negative_passages.docid: 77071
negative_passages.text: Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$
negative_passages.docid: 141795
negative_passages.text: Solve the second order ODE $(2x^2 + 1)y'' − 4xy' + 4y = 0$
negative_passages.docid: 9143
negative_passages.text: Solve $u_{xx}-3u_{xt}-4u_{tt}=0$ where $u(x,0)=x^2$ and $u_t(x,0)=e^x$
negative_passages.docid: 106609
negative_passages.text: Show that $e^{iy} = 1 + iy + \frac{\mu_1 y^2}{2}$ for all $y \in \mathbb{R}$ with $|\mu_1| \leq 1$
negative_passages.docid: 78719
negative_passages.text: Solve the DE $yy^{\prime}+x=\sqrt{x^2+y^2}$