query: Having difficulty solving ODE: $y' = \frac{1}{2} a y^2 + b y - 1$ with $y(0)=0$
positive_passages.docid: 145504
positive_passages.text: Help solving variable separable ODE: $y' = \frac{1}{2} a y^2 + b y - 1$ with $y(0)=0$
negative_passages.docid: 144841
negative_passages.text: Find general solution $y''y^3=1$
negative_passages.docid: 132108
negative_passages.text: How to solve differential equation $y=xy'+\frac12y'^2$
negative_passages.docid: 158938
negative_passages.text: Using DSolve to solve for x[t,parameter]
negative_passages.docid: 38894
negative_passages.text: Solve $x=y\frac{dy}{dx}-\left(\frac{dy}{dx}\right)^{2}$
negative_passages.docid: 81437
negative_passages.text: Find the value of $y(1)$ of the ODE $y'+y=|x|$.
negative_passages.docid: 114861
negative_passages.text: equation $\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x^2}+\frac{1}{y^2}}$
negative_passages.docid: 114505
negative_passages.text: Initial value problem $t\frac{dx}{dt}=x+\sqrt{t^2+x^2}$
negative_passages.docid: 30120
negative_passages.text: Find solutions for an differential equation system
negative_passages.docid: 71465
negative_passages.text: solution of $y' = \exp \left(-\frac yx\right) + \frac yx$
negative_passages.docid: 84689
negative_passages.text: solving third-order nonlinear ordinary differential equation
negative_passages.docid: 60396
negative_passages.text: How to Solve the Coupled Differential Equations?
negative_passages.docid: 11707
negative_passages.text: If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$
negative_passages.docid: 41720
negative_passages.text: Getting equation from differential equations
negative_passages.docid: 58083
negative_passages.text: what can I say about the solution $y(x)$ of the ODE?
negative_passages.docid: 67158
negative_passages.text: Solve $y'-\int_0^xy(t)dt=2$
negative_passages.docid: 72872
negative_passages.text: Number of zeroes of solution to $y''(x)+e^{x^2}y(x)=0$ in $[0,3π]$